Artículos de revistas: "Milnor"

1

Point, Françoise;. "Milnor identities". Communications in Algebra 24, n.º 12 (enero de 1996): 3725–44. http://dx.doi.org/10.1080/00927879608825783.

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2

Caubel, Clément, András Némethi y Patrick Popescu-Pampu. "Milnor open books and Milnor fillable contact 3-manifolds". Topology 45, n.º 3 (mayo de 2006): 673–89. http://dx.doi.org/10.1016/j.top.2006.01.002.

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3

Mond, David y Duco van Straten. "KNOTTED MILNOR FIBRES". Topology 38, n.º 4 (julio de 1999): 915–29. http://dx.doi.org/10.1016/s0040-9383(98)00038-x.

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4

Matsui, Yutaka y Kiyoshi Takeuchi. "Motivic Milnor Fibers and Jordan Normal Forms of Milnor Monodromies". Publications of the Research Institute for Mathematical Sciences 50, n.º 2 (2014): 207–26. http://dx.doi.org/10.4171/prims/130.

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5

Ruas, Maria Aparecida Soares y Miriam Da Silva Pereira. "Codimension Two Determinantal Varieties with Isolated Singularities". MATHEMATICA SCANDINAVICA 115, n.º 2 (3 de diciembre de 2014): 161. http://dx.doi.org/10.7146/math.scand.a-19220.

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We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in $\mathsf{C}^4$, we obtain a Lê-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the $1$-form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from Frühbis-Krüger and Neumer [7] list of simple determinantal surface singularities.

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6

Cisneros-Molina, José Luis y Aurélio Menegon. "Equivalence of Milnor and Milnor-Lê fibrations for real analytic maps". International Journal of Mathematics 30, n.º 14 (20 de noviembre de 2019): 1950078. http://dx.doi.org/10.1142/s0129167x19500782.

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In [J. Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61 (Princeton University Press, Princeton, NJ, 1968).] Milnor proved that a real analytic map [Formula: see text], where [Formula: see text], with an isolated critical point at the origin has a fibration on the tube [Formula: see text]. Constructing a vector field such that (1) it is transverse to the spheres, and (2) it is transverse to the tubes, he “inflates” the tube to the sphere, to get a fibration [Formula: see text], but the projection is not necessarily given by [Formula: see text] as in the complex case. In the case [Formula: see text] has isolated critical value, in [J. L. Cisneros-Molina, J. Seade and J. Snoussi, Milnor fibrations and [Formula: see text]-regularity for real analytic singularities, Internat. J. Math. 21(4) (2010) 419–434.] it was proved that if the fibers inside a small tube are transverse to the sphere [Formula: see text], then it has a fibration on the tube. Also in [J. L. Cisneros-Molina, J. Seade and J. Snoussi, Milnor fibrations and [Formula: see text]-regularity for real analytic singularities, Internat. J. Math. 21(4) (2010) 419–434.], the concept of [Formula: see text]-regularity was defined, it turns out that [Formula: see text] is [Formula: see text]-regular if and only if the map [Formula: see text] is a fiber bundle equivalent to the one on the tube. In a more general setting, the corresponding facts are proved in [J. L. Cisneros-Molina, A. Menegon, J. Seade and J. Snoussi, Fibration theorems and [Formula: see text]-regularity for differentiable maps-germs with non-isolated critical value, Preprint (2017).], showing that if a locally surjective map [Formula: see text] has a linear discriminant [Formula: see text] with isolated singularity and a fibration on the tube [Formula: see text], then [Formula: see text] is [Formula: see text]-regular if and only if the map [Formula: see text] (with [Formula: see text] the radial projection of [Formula: see text] on [Formula: see text]) is a fiber bundle equivalent to the one on the tube. In this paper, we generalize this result for an arbitrary linear discriminant by constructing a vector field [Formula: see text] which inflates the tube to the sphere in a controlled way, it satisfies properties analogous to the vector field constructed by Milnor in the complex setting: besides satisfying (1) and (2) above, it also satisfies that [Formula: see text] is constant on the integral curves of [Formula: see text].

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7

Feld, Niels. "Milnor-Witt cycle modules". Journal of Pure and Applied Algebra 224, n.º 7 (julio de 2020): 106298. http://dx.doi.org/10.1016/j.jpaa.2019.106298.

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8

Shilin, I. S. "Lyapunov unstable milnor attractors". Doklady Mathematics 94, n.º 1 (julio de 2016): 415–17. http://dx.doi.org/10.1134/s1064562416040165.

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9

Meng, Guowu y Clifford Henry Taubes. "$\underline{SW}$ = Milnor Torsion". Mathematical Research Letters 3, n.º 5 (1996): 661–74. http://dx.doi.org/10.4310/mrl.1996.v3.n5.a8.

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10

Raussen, Martin y Christian Skau. "Interview with John Milnor". Notices of the American Mathematical Society 59, n.º 03 (1 de marzo de 2012): 400. http://dx.doi.org/10.1090/noti803.

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11

Orlik, Peter y Hiroaki Terao. "Arrangements and Milnor fibers". Mathematische Annalen 301, n.º 1 (enero de 1995): 211–35. http://dx.doi.org/10.1007/bf01446627.

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12

Bodin, Arnaud. "Jump of Milnor numbers". Bulletin of the Brazilian Mathematical Society, New Series 38, n.º 3 (septiembre de 2007): 389–96. http://dx.doi.org/10.1007/s00574-007-0051-4.

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13

Massey, David B. "Hypercohomology of Milnor fibres". Topology 35, n.º 4 (octubre de 1996): 969–1003. http://dx.doi.org/10.1016/0040-9383(95)00054-2.

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14

Némethi, András y Alexandru Zaharia. "Milnor fibration at infinity". Indagationes Mathematicae 3, n.º 3 (1992): 323–35. http://dx.doi.org/10.1016/0019-3577(92)90039-n.

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15

Wang, Zhenjian. "Deformation of Milnor algebras". Pacific Journal of Mathematics 305, n.º 1 (17 de marzo de 2020): 329–38. http://dx.doi.org/10.2140/pjm.2020.305.329.

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16

Wada, Kodai y Akira Yasuhara. "Milnor invariants of clover links". International Journal of Mathematics 27, n.º 13 (diciembre de 2016): 1650108. http://dx.doi.org/10.1142/s0129167x16501081.

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Levine introduced clover links to investigate the indeterminacy of Milnor invariants of links. He proved that for a clover link, Milnor numbers of length up to [Formula: see text] are well-defined if those of length [Formula: see text] vanish, and that Milnor numbers of length at least [Formula: see text] are not well-defined if those of length [Formula: see text] survive. For a clover link [Formula: see text] with vanishing Milnor numbers of length [Formula: see text], we show that the Milnor number [Formula: see text] for a sequence [Formula: see text] is well-defined by taking modulo the greatest common divisor of the [Formula: see text], where [Formula: see text] is any proper subsequence of [Formula: see text] obtained by removing at least [Formula: see text] indices. Moreover, if [Formula: see text] is a non-repeated sequence of length [Formula: see text], the possible range of [Formula: see text] is given explicitly. As an application, we give an edge-homotopy classification of [Formula: see text]-clover links.

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17

BHUPAL, MOHAN. "OPEN BOOK DECOMPOSITIONS OF LINKS OF SIMPLE SURFACE SINGULARITIES". International Journal of Mathematics 20, n.º 12 (diciembre de 2009): 1527–45. http://dx.doi.org/10.1142/s0129167x09005868.

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We describe open book decompositions of links of simple surface singularities that support the corresponding unique Milnor fillable contact structures. The open books we describe are isotopic to Milnor open books.

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18

CISNEROS-MOLINA, J. L., J. SEADE y J. SNOUSSI. "MILNOR FIBRATIONS AND d-REGULARITY FOR REAL ANALYTIC SINGULARITIES". International Journal of Mathematics 21, n.º 04 (abril de 2010): 419–34. http://dx.doi.org/10.1142/s0129167x10006124.

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We study Milnor fibrations of real analytic maps [Formula: see text], n ≥ p, with an isolated critical value. We do so by looking at a pencil associated canonically to every such map, with axis V = f-1(0). The elements of this pencil are all analytic varieties with singular set contained in V. We introduce the concept of d-regularity, which means that away from the axis each element of the pencil is transverse to all sufficiently small spheres. We show that if V has dimension 0, or if f has the Thom af-property, then f is d-regular if and only if it has a Milnor fibration on every sufficiently small sphere, with projection map f/‖f‖. Our results include the case when f has an isolated critical point. Furthermore, we show that if f is d-regular, then its Milnor fibration on the sphere is equivalent to its fibration on a Milnor tube. To prove these fibration theorems we introduce the spherefication map, which is rather useful to study Milnor fibrations. It is defined away from V; one of its main properties is that it is a submersion if and only if f is d-regular. Here restricted to each sphere in ℝn the spherefication gives a fiber bundle equivalent to the Milnor fibration.

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19

Cisneros-Molina, José Luis y Aurélio Menegon. "Errata to equivalence of Milnor and Milnor–Lê fibrations for real analytic maps". International Journal of Mathematics 32, n.º 10 (8 de julio de 2021): 2150070. http://dx.doi.org/10.1142/s0129167x21500701.

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In the proof of Theorem 3.7 of the original paper Internat. J. Math. 30(14) (2019) 1950078, 1–25, two inequalities are used that do not hold in general. In this note, we prove an extra propositions which allows us to give a proof of Theorem 3.7 without using the aforementioned inequalities. Hence, all the results in the original paper are valid. We have also posted a corrected version in the arXiv.

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20

Cohen, Daniel C., Graham Denham y Alexander I. Suciu. "Torsion in Milnor fiber homology". Algebraic & Geometric Topology 3, n.º 1 (15 de junio de 2003): 511–35. http://dx.doi.org/10.2140/agt.2003.3.511.

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21

Bucher, Michelle y Tsachik Gelander. "Milnor–Wood inequalities for products". Algebraic & Geometric Topology 13, n.º 3 (18 de mayo de 2013): 1733–42. http://dx.doi.org/10.2140/agt.2013.13.1733.

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22

Kobayashi, Natsuka, Kodai Wada y Akira Yasuhara. "Milnor invariants of covering links". Topology and its Applications 224 (junio de 2017): 60–72. http://dx.doi.org/10.1016/j.topol.2017.04.002.

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23

Brady, Thomas, Michael Falk y Colum Watt. "Noncrossing partitions and Milnor fibers". Algebraic & Geometric Topology 18, n.º 7 (11 de diciembre de 2018): 3821–38. http://dx.doi.org/10.2140/agt.2018.18.3821.

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24

Cohen, Daniel C. y Alexander I. Suciu. "On Milnor Fibrations of Arrangements". Journal of the London Mathematical Society 51, n.º 1 (febrero de 1995): 105–19. http://dx.doi.org/10.1112/jlms/51.1.105.

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25

Vial, Charles. "Operations in Milnor K-theory". Journal of Pure and Applied Algebra 213, n.º 7 (julio de 2009): 1325–45. http://dx.doi.org/10.1016/j.jpaa.2008.12.001.

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26

Fleming, Thomas. "Milnor invariants for spatial graphs". Topology and its Applications 155, n.º 12 (junio de 2008): 1297–305. http://dx.doi.org/10.1016/j.topol.2008.03.010.

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27

Bodin, Arnaud, Anne Pichon y José Seade. "Milnor fibrations of meromorphic functions". Journal of the London Mathematical Society 80, n.º 2 (15 de junio de 2009): 311–25. http://dx.doi.org/10.1112/jlms/jdp027.

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28

Suciu, Alexander. "Hyperplane arrangements and Milnor fibrations". Annales de la faculté des sciences de Toulouse Mathématiques 23, n.º 2 (2014): 417–81. http://dx.doi.org/10.5802/afst.1412.

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29

Massey, David B. y Le Dung Trang. "Hypersurface Singularities and Milnor Equisingularity". Pure and Applied Mathematics Quarterly 2, n.º 3 (2006): 893–914. http://dx.doi.org/10.4310/pamq.2006.v2.n3.a13.

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30

MELLOR, BLAKE. "WEIGHT SYSTEMS FOR MILNOR INVARIANTS". Journal of Knot Theory and Its Ramifications 17, n.º 02 (febrero de 2008): 213–30. http://dx.doi.org/10.1142/s0218216508006063.

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We use Polyak's skein relation to give a new proof that Milnor's string link invariants μ12⋯n are finite type invariants, and to develop a recursive relation for their associated weight systems. We show that the obstruction to the triviality of these weight systems is the presence of a certain kind of spanning tree in the intersection graph of a chord diagram.

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31

HSIEH, CHUN-CHUNG. "COMBINATORIC MASSEY–MILNOR LINKING THEORY". Journal of Knot Theory and Its Ramifications 20, n.º 06 (junio de 2011): 927–38. http://dx.doi.org/10.1142/s0218216511009030.

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In this paper following the scheme of Massey–Milnor invariant theory [C. C. Hsieh, Combinatoric and diagrammatic studies in knot theory J. Knot Theory Ramifications16 (2007) 1235–1253; C. C. Hsieh, Massey-Milnor linking = Chern-Simons-Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903; C. C. Hsieh and S. W. Yang, Chern-Simons-Witten configuration space integrals in knot theory, J. Knot Theory Ramifications14 (2005) 689–711], we studied the first non-vanishing linkings of knot theory in ℝ3 and also derived the combinatorial formulae from which we could read out the invariants directly from the knot diagrams. Though the theme is calculus, the idea comes from perturbative quantum field theory.

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32

Lewis, James D. "Real Regulators on Milnor Complexes". K-Theory 25, n.º 3 (marzo de 2002): 277–98. http://dx.doi.org/10.1023/a:1015696107010.

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33

Fichou, Goulwen. "The motivic real Milnor fibres". Manuscripta Mathematica 139, n.º 1-2 (6 de diciembre de 2011): 167–78. http://dx.doi.org/10.1007/s00229-011-0511-4.

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34

Kerz, Moritz y Stefan Müller-Stach. "The Milnor–Chow homomorphism revisited". K-Theory 38, n.º 1 (noviembre de 2007): 49–58. http://dx.doi.org/10.1007/s10977-007-9006-1.

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35

Callejas-Bedregal, R., M. F. Z. Morgado y J. Seade. "Lê cycles and Milnor classes". Inventiones mathematicae 197, n.º 2 (19 de enero de 2013): 453–82. http://dx.doi.org/10.1007/s00222-013-0450-7.

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36

Seade, José, Mihai Tibăr y Alberto Verjovsky. "Milnor numbers and Euler obstruction*". Bulletin of the Brazilian Mathematical Society, New Series 36, n.º 2 (julio de 2005): 275–83. http://dx.doi.org/10.1007/s00574-005-0039-x.

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37

Melle-Hernández, A. "Milnor numbers for surface singularities". Israel Journal of Mathematics 115, n.º 1 (diciembre de 2000): 29–50. http://dx.doi.org/10.1007/bf02810579.

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38

Dimca, Alexandru. "Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements". Nagoya Mathematical Journal 206 (junio de 2012): 75–97. http://dx.doi.org/10.1017/s0027763000010540.

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AbstractThe order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given.It is known that the complement of a complex hyperplane arrangement is cohomologically Tate and, if the arrangement is defined over ℚ, has polynomial count. We show that these properties hold for the corresponding Milnor fibers if the monodromy is trivial.We construct a hyperplane arrangement defined over ℚ, whose Milnor fiber has a nontrivial monodromy operator, is cohomologically Tate, and has no polynomial count. Such examples are shown not to exist in low dimensions.

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39

Dimca, Alexandru. "Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements". Nagoya Mathematical Journal 206 (junio de 2012): 75–97. http://dx.doi.org/10.1215/00277630-1548502.

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AbstractThe order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and sufficient condition for the triviality of this monodromy operator is given.It is known that the complement of a complex hyperplane arrangement is cohomologically Tate and, if the arrangement is defined over ℚ, has polynomial count. We show that these properties hold for the corresponding Milnor fibers if the monodromy is trivial.We construct a hyperplane arrangement defined over ℚ, whose Milnor fiber has a nontrivial monodromy operator, is cohomologically Tate, and has no polynomial count. Such examples are shown not to exist in low dimensions.

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40

Aguilar-Cabrera, Haydée. "Open-book decompositions of 𝕊5 and real singularities". International Journal of Mathematics 25, n.º 09 (agosto de 2014): 1450085. http://dx.doi.org/10.1142/s0129167x14500852.

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In this article, we study the topology of the family of real analytic germs F : (ℂ3, 0) → (ℂ, 0) given by [Formula: see text] with p, q, r ∈ ℕ, p, q, r ≥ 2 and (p, q) = 1. Such a germ has an isolated singularity at 0 and gives rise to a Milnor fibration [Formula: see text]. Moreover, it is known that the link LF is a Seifert manifold and that it is always homeomorphic to the link of a complex singularity. However, we prove that in almost all the cases the open-book decomposition of 𝕊5 given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in ℂ3.

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41

Kreinbihl, James. "A Fox–Milnor theorem for knots in a thickened surface". Journal of Knot Theory and Its Ramifications 28, n.º 12 (octubre de 2019): 1950073. http://dx.doi.org/10.1142/s0218216519500731.

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A knot in a thickened surface [Formula: see text] is a smooth embedding [Formula: see text], where [Formula: see text] is a closed, connected, orientable surface. There is a bijective correspondence between knots in [Formula: see text] and knots in [Formula: see text], so one can view the study of knots in thickened surfaces as an extension of classical knot theory. An immediate question is if other classical definitions, concepts, and results extend or generalize to the study of knots in a thickened surface. One such famous result is the Fox–Milnor Theorem, which relates the Alexander polynomials of concordant knots. We prove a Fox–Milnor Theorem for concordant knots in a thickened surface by using Milnor torsion.

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42

Némethi, András y Meral Tosun. "Invariants of open books of links of surface singularities". Studia Scientiarum Mathematicarum Hungarica 48, n.º 1 (1 de marzo de 2011): 135–44. http://dx.doi.org/10.1556/sscmath.2010.1159.

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If M is the link of a complex normal surface singularity, then it carries a canonical contact structure ξcan, which can be identified from the topology of the 3-manifold M. We assume that M is a rational homology sphere. We compute the support genus, the binding number and the norm associated with the open books which support ζcan, provided that we restrict ourselves to the case of (analytic) Milnor open books. In order to do this, we determine monotonity properties of the genus and the Milnor number of all Milnor fibrations in terms of the Lipman cone.We generalize results of [3] valid for links of rational surface singularities, and we answer some questions of Etnyre and Ozbagci [7, section 8] regarding the above invariants.

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43

Tsutsui, Daiji. "Center Manifold Analysis of Plateau Phenomena Caused by Degeneration of Three-Layer Perceptron". Neural Computation 32, n.º 4 (abril de 2020): 683–710. http://dx.doi.org/10.1162/neco_a_01268.

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A hierarchical neural network usually has many singular regions in the parameter space due to the degeneration of hidden units. Here, we focus on a three-layer perceptron, which has one-dimensional singular regions comprising both attractive and repulsive parts. Such a singular region is often called a Milnor-like attractor. It is empirically known that in the vicinity of a Milnor-like attractor, several parameters converge much faster than the rest and that the dynamics can be reduced to smaller-dimensional ones. Here we give a rigorous proof for this phenomenon based on a center manifold theory. As an application, we analyze the reduced dynamics near the Milnor-like attractor and study the stochastic effects of the online learning.

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44

Kotorii, Yuka y Akira Yasuhara. "Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length ≤k". Topology and its Applications 184 (abril de 2015): 87–100. http://dx.doi.org/10.1016/j.topol.2015.01.003.

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45

Menegon Neto, Aurélio. "Lê's polyhedron for line singularities". International Journal of Mathematics 25, n.º 13 (diciembre de 2014): 1450114. http://dx.doi.org/10.1142/s0129167x14501146.

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We study the topology of line singularities, which are complex hypersurface germs with non-isolated singularity given by a smooth curve. We describe the degeneration of its Milnor fiber to the singular hypersurface by means of a vanishing polyhedron in the Milnor fiber. As a milestone, we also study the topology of the degeneration of a complex isolated singularity hypersurface under a nonlocal point of view.

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46

Rudenko, Daniil. "The strong Suslin reciprocity law". Compositio Mathematica 157, n.º 4 (abril de 2021): 649–76. http://dx.doi.org/10.1112/s0010437x20007666.

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We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$ -theory. The Milnor $K$ -groups can be identified with the top cohomology groups of the polylogarithmic motivic complexes; Goncharov's conjecture predicts the existence of a contracting homotopy underlying Suslin reciprocity. The main ingredient of the proof is a homotopy invariance theorem for the cohomology of the polylogarithmic motivic complexes in the ‘next to Milnor’ degree. We apply these results to the theory of scissors congruences of hyperbolic polytopes. For every triple of rational functions on a compact projective curve over $\mathbb {C}$ we construct a hyperbolic polytope (defined up to scissors congruence). The hyperbolic volume and the Dehn invariant of this polytope can be computed directly from the triple of rational functions on the curve.

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47

Minakawa, Hiroyuki. "Milnor-Wood inequality for crystallographic groups". Séminaire de théorie spectrale et géométrie 13 (1995): 167–70. http://dx.doi.org/10.5802/tsg.160.

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48

Langevin, Rémi y Françoise Michel. "Nombres de Milnor d'un entrelacs Brunnien". Bulletin de la Société mathématique de France 79 (1985): 53–77. http://dx.doi.org/10.24033/bsmf.2020.

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49

Grove, Karsten y Wolfgang Ziller. "Curvature and Symmetry of Milnor Spheres". Annals of Mathematics 152, n.º 1 (julio de 2000): 331. http://dx.doi.org/10.2307/2661385.

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50

Goulwen Fichou y Masahiro Shiota. "Real Milnor Fibres and Puiseux Series". Annales scientifiques de l'École normale supérieure 50, n.º 5 (2017): 1205–40. http://dx.doi.org/10.24033/asens.2343.

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Artículos de revistas sobre el tema "Milnor"

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