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Artículos de revistas sobre el tema "Milnor"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 1 de febrero de 2022

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1

Point, Françoise;. "Milnor identities." Communications in Algebra 24, no. 12 (1996): 3725–44. http://dx.doi.org/10.1080/00927879608825783.

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2

Caubel, Clément, András Némethi, and Patrick Popescu-Pampu. "Milnor open books and Milnor fillable contact 3-manifolds." Topology 45, no. 3 (2006): 673–89. http://dx.doi.org/10.1016/j.top.2006.01.002.

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3

Mond, David, and Duco van Straten. "KNOTTED MILNOR FIBRES." Topology 38, no. 4 (1999): 915–29. http://dx.doi.org/10.1016/s0040-9383(98)00038-x.

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4

Matsui, Yutaka, and Kiyoshi Takeuchi. "Motivic Milnor Fibers and Jordan Normal Forms of Milnor Monodromies." Publications of the Research Institute for Mathematical Sciences 50, no. 2 (2014): 207–26. http://dx.doi.org/10.4171/prims/130.

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5

Ruas, Maria Aparecida Soares, and Miriam Da Silva Pereira. "Codimension Two Determinantal Varieties with Isolated Singularities." MATHEMATICA SCANDINAVICA 115, no. 2 (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

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6

Cisneros-Molina, José Luis, and Aurélio Menegon. "Equivalence of Milnor and Milnor-Lê fibrations for real analytic maps." International Journal of Mathematics 30, no. 14 (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 co

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7

Feld, Niels. "Milnor-Witt cycle modules." Journal of Pure and Applied Algebra 224, no. 7 (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, no. 1 (2016): 415–17. http://dx.doi.org/10.1134/s1064562416040165.

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9

Meng, Guowu, and Clifford Henry Taubes. "$\underline{SW}$ = Milnor Torsion." Mathematical Research Letters 3, no. 5 (1996): 661–74. http://dx.doi.org/10.4310/mrl.1996.v3.n5.a8.

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10

Raussen, Martin, and Christian Skau. "Interview with John Milnor." Notices of the American Mathematical Society 59, no. 03 (2012): 400. http://dx.doi.org/10.1090/noti803.

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11

Orlik, Peter, and Hiroaki Terao. "Arrangements and Milnor fibers." Mathematische Annalen 301, no. 1 (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, no. 3 (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, no. 4 (1996): 969–1003. http://dx.doi.org/10.1016/0040-9383(95)00054-2.

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14

Némethi, András, and Alexandru Zaharia. "Milnor fibration at infinity." Indagationes Mathematicae 3, no. 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, no. 1 (2020): 329–38. http://dx.doi.org/10.2140/pjm.2020.305.329.

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16

Wada, Kodai, and Akira Yasuhara. "Milnor invariants of clover links." International Journal of Mathematics 27, no. 13 (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 gr

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17

BHUPAL, MOHAN. "OPEN BOOK DECOMPOSITIONS OF LINKS OF SIMPLE SURFACE SINGULARITIES." International Journal of Mathematics 20, no. 12 (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, and J. SNOUSSI. "MILNOR FIBRATIONS AND d-REGULARITY FOR REAL ANALYTIC SINGULARITIES." International Journal of Mathematics 21, no. 04 (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

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19

Cisneros-Molina, José Luis, and Aurélio Menegon. "Errata to equivalence of Milnor and Milnor–Lê fibrations for real analytic maps." International Journal of Mathematics 32, no. 10 (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, and Alexander I. Suciu. "Torsion in Milnor fiber homology." Algebraic & Geometric Topology 3, no. 1 (2003): 511–35. http://dx.doi.org/10.2140/agt.2003.3.511.

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21

Bucher, Michelle, and Tsachik Gelander. "Milnor–Wood inequalities for products." Algebraic & Geometric Topology 13, no. 3 (2013): 1733–42. http://dx.doi.org/10.2140/agt.2013.13.1733.

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22

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

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23

Brady, Thomas, Michael Falk, and Colum Watt. "Noncrossing partitions and Milnor fibers." Algebraic & Geometric Topology 18, no. 7 (2018): 3821–38. http://dx.doi.org/10.2140/agt.2018.18.3821.

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24

Cohen, Daniel C., and Alexander I. Suciu. "On Milnor Fibrations of Arrangements." Journal of the London Mathematical Society 51, no. 1 (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, no. 7 (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, no. 12 (2008): 1297–305. http://dx.doi.org/10.1016/j.topol.2008.03.010.

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27

Bodin, Arnaud, Anne Pichon, and José Seade. "Milnor fibrations of meromorphic functions." Journal of the London Mathematical Society 80, no. 2 (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, no. 2 (2014): 417–81. http://dx.doi.org/10.5802/afst.1412.

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29

Massey, David B., and Le Dung Trang. "Hypersurface Singularities and Milnor Equisingularity." Pure and Applied Mathematics Quarterly 2, no. 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, no. 02 (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, no. 06 (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

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32

Lewis, James D. "Real Regulators on Milnor Complexes." K-Theory 25, no. 3 (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, no. 1-2 (2011): 167–78. http://dx.doi.org/10.1007/s00229-011-0511-4.

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34

Kerz, Moritz, and Stefan Müller-Stach. "The Milnor–Chow homomorphism revisited." K-Theory 38, no. 1 (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, and J. Seade. "Lê cycles and Milnor classes." Inventiones mathematicae 197, no. 2 (2013): 453–82. http://dx.doi.org/10.1007/s00222-013-0450-7.

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36

Seade, José, Mihai Tibăr, and Alberto Verjovsky. "Milnor numbers and Euler obstruction*." Bulletin of the Brazilian Mathematical Society, New Series 36, no. 2 (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, no. 1 (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 (June 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 o

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39

Dimca, Alexandru. "Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements." Nagoya Mathematical Journal 206 (June 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 o

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40

Aguilar-Cabrera, Haydée. "Open-book decompositions of 𝕊5 and real singularities". International Journal of Mathematics 25, № 09 (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, no. 12 (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 polynom

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42

Némethi, András, and Meral Tosun. "Invariants of open books of links of surface singularities." Studia Scientiarum Mathematicarum Hungarica 48, no. 1 (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 li

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43

Tsutsui, Daiji. "Center Manifold Analysis of Plateau Phenomena Caused by Degeneration of Three-Layer Perceptron." Neural Computation 32, no. 4 (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 the

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44

Kotorii, Yuka, and Akira Yasuhara. "Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length ≤k." Topology and its Applications 184 (April 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, no. 13 (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, no. 4 (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

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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, and 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, and Wolfgang Ziller. "Curvature and Symmetry of Milnor Spheres." Annals of Mathematics 152, no. 1 (2000): 331. http://dx.doi.org/10.2307/2661385.

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50

Goulwen Fichou and Masahiro Shiota. "Real Milnor Fibres and Puiseux Series." Annales scientifiques de l'École normale supérieure 50, no. 5 (2017): 1205–40. http://dx.doi.org/10.24033/asens.2343.

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