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Relevant bibliographies by topics / Alexander polynomial

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Academic literature on the topic 'Alexander polynomial'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Alexander polynomial"

1

JIN, XIAN'AN, and FUJI ZHANG. "ALEXANDER POLYNOMIAL FOR EVEN GRAPHS WITH REFLECTIVE SYMMETRY." Journal of Knot Theory and Its Ramifications 17, no. 10 (2008): 1241–56. http://dx.doi.org/10.1142/s0218216508006610.

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Based on the connection with Alexander polynomial of special alternating links, Murasugi and Stoimenow introduced the Alexander polynomial of even graphs. In this paper, we study the Alexander polynomial of spatial even graphs with reflective symmetry. Roughly speaking, we prove that the Alexander polynomial of one half of a spatial even graph with reflective symmetry is a divisor of that of the whole spatial even graph. Then, we apply the result to a family of special alternating links, expressing the Alexander polynomial of such a link as the product of Alexander polynomials of two smaller s

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Nguyen, Hoang-An, and Anh T. Tran. "Adjoint twisted Alexander polynomial of twisted Whitehead links." Journal of Knot Theory and Its Ramifications 27, no. 04 (2018): 1850026. http://dx.doi.org/10.1142/s0218216518500268.

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The adjoint twisted Alexander polynomial has been computed for twist knots [A. Tran, Twisted Alexander polynomials with the adjoint action for some classes of knots, J. Knot Theory Ramifications 23(10) (2014) 1450051], genus one two-bridge knots [A. Tran, Adjoint twisted Alexander polynomials of genus one two-bridge knots, J. Knot Theory Ramifications 25(10) (2016) 1650065] and the Whitehead link [J. Dubois and Y. Yamaguchi, Twisted Alexander invariant and nonabelian Reidemeister torsion for hyperbolic three dimensional manifolds with cusps, Preprint (2009), arXiv:0906.1500 ]. In this paper, w

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CRANS, ALISSA S., ALLISON HENRICH, and SAM NELSON. "POLYNOMIAL KNOT AND LINK INVARIANTS FROM THE VIRTUAL BIQUANDLE." Journal of Knot Theory and Its Ramifications 22, no. 04 (2013): 1340004. http://dx.doi.org/10.1142/s021821651340004x.

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The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which determine both the generalized Alexander polynomial (also known as the Sawollek polynomial) for virtual knots and the classical Alexander polynomial for classical knots. For a fixed monomial ordering <, the Gröbner bases for these ideals are computable, comparable invariants which fully determine the elementary ideals and which generalize and unify the classi

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YAMANAKA, HITOSHI. "WEIGHTS OF MARKOV TRACES OF ALEXANDER POLYNOMIALS FOR MIXED LINKS." Journal of Knot Theory and Its Ramifications 22, no. 07 (2013): 1350028. http://dx.doi.org/10.1142/s0218216513500284.

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Using the Fourier expansion of Markov traces for Ariki–Koike algebras over ℚ(q, u1, …, ue), we give a direct definition of the Alexander polynomials for mixed links. We observe that under the corresponding specialization of a Markov parameter, the Fourier coefficients of Markov traces take quite a simple form. As a consequence, we show that the Alexander polynomial of a mixed link is essentially equal to the Alexander polynomial of the link obtained by resolving the twisted parts.

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Mellor, Blake. "Alexander and writhe polynomials for virtual knots." Journal of Knot Theory and Its Ramifications 25, no. 08 (2016): 1650050. http://dx.doi.org/10.1142/s0218216516500504.

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We give a new interpretation of the Alexander polynomial [Formula: see text] for virtual knots due to Sawollek [On Alexander–Conway polynomials for virtual knots and Links, preprint (2001), arXiv:math/9912173] and Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications 12 (2003) 987–1000], and use it to show that, for any virtual knot, [Formula: see text] determines the writhe polynomial of Cheng and Gao [A polynomial invariant of virtual links, J. Knot Theory Ramifications 22(12) (2013), Article ID: 1341002, 33pp.] (equivalently, Kauffman’s affine index polyn

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DEGTYAREV, ALEXANDER. "ALEXANDER POLYNOMIAL OF A CURVE OF DEGREE SIX." Journal of Knot Theory and Its Ramifications 03, no. 04 (1994): 439–54. http://dx.doi.org/10.1142/s0218216594000320.

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The complete description of the Alexander polynomial of the complement of an irreducible sextic in [Formula: see text] is given. Some general results about Alexander polynomials of algebraic curves are also obtained.

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Conway, Anthony. "Burau Maps and Twisted Alexander Polynomials." Proceedings of the Edinburgh Mathematical Society 61, no. 2 (2018): 479–97. http://dx.doi.org/10.1017/s0013091517000128.

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AbstractThe Burau representation of the braid group can be used to recover the Alexander polynomial of the closure of a braid. We define twisted Burau maps and use them to compute twisted Alexander polynomials.

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Jiménez Pascual, Adrián. "On lassos and the Jones polynomial of satellite knots." Journal of Knot Theory and Its Ramifications 25, no. 02 (2016): 1650011. http://dx.doi.org/10.1142/s0218216516500115.

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In this paper, I present a new family of knots in the solid torus called lassos, and their properties. Given a knot [Formula: see text] with Alexander polynomial [Formula: see text], I then use these lassos as patterns to construct families of satellite knots that have Alexander polynomial [Formula: see text] where [Formula: see text]. In particular, I prove that if [Formula: see text] these satellite knots have different Jones polynomials.

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Fukuhara, Shinji. "Explicit formulae for two-bridge knot polynomials." Journal of the Australian Mathematical Society 78, no. 2 (2005): 149–66. http://dx.doi.org/10.1017/s1446788700008004.

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AbstractA two-bridge knot (or link) can be characterized by the so-called Schubert normal formKp, qwherepandqare positive coprime integers. Associated toKp, qthere are the Conway polynomial ▽kp, q(z)and the normalized Alexander polynomial Δkp, q(t). However, it has been open problem how ▽kp, q(z) and Δkp, q(t) are expressed in terms ofpandq. In this note, we will give explicit formulae for the Conway polynomials and the normalized Alexander polynomials in the case of two-bridge knots and links. This is done using elementary number theoretical functions inpandq.

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Boden, Hans U., Emily Dies, Anne Isabel Gaudreau, Adam Gerlings, Eric Harper, and Andrew J. Nicas. "Alexander invariants for virtual knots." Journal of Knot Theory and Its Ramifications 24, no. 03 (2015): 1550009. http://dx.doi.org/10.1142/s0218216515500091.

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Given a virtual knot K, we introduce a new group-valued invariant VGK called the virtual knot group, and we use the elementary ideals of VGK to define invariants of K called the virtual Alexander invariants. For instance, associated to the zeroth ideal is a polynomial HK(s, t, q) in three variables which we call the virtual Alexander polynomial, and we show that it is closely related to the generalized Alexander polynomial GK(s, t) introduced by Sawollek; Kauffman and Radford; and Silver and Williams. We define a natural normalization of the virtual Alexander polynomial and show it satisfies a

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Dissertations / Theses on the topic "Alexander polynomial"

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Lipson, Andrew Solomon. "Polynomial invariants of knots and links." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303206.

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Woodard, Mary Kay. "Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc501096/.

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The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots are equivalent, as defined in this investigation, then they receive identical polynomials. Yet, if two knots have identical polynomials, no information about their equivalence may be obtained. To define the Conway polynomial, the Axioms for Computation are given and many examples of their use are includ

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Alcaraz, Karin. "The Alexander polynomial of closed 3-manifolds." Thesis, University of Oxford, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.564280.

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Black, Samson 1979. "Representations of Hecke algebras and the Alexander polynomial." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10847.

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viii, 50 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the Markov trace which descends to STLd. Combining this point of view with Ocneanu's formula for the Markov trace and Young's seminormal form, we deduce a new state-sum formula for the Alexander polynomial. We also give a direct combi

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Watanabe, Tadayuki. "Configuration space integral for long n-knots and the Alexander polynomial." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/136744.

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Venturelli, Federico. "The Alexander polynomial of certain classes of non-symmetric line arrangements." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3422691.

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The Alexander polynomial of a projective hypersurface V ϲ Pᶰ is the characteristic polynomial of the monodromy operator acting on Hᶰ¯¹(F, C), where F is the Milnor fibre of V; unless V is smooth, the problem of its computation is open. The singular hypersurfaces that have drawn the most attention are projectivisations Ᾱ of central hyperplane arrangements A C Cᶰ⁺ ¹, as one can hope to take advantage of the combinatorial nature of such objects; one can assume without loss of generality that n=2. In this Thesis we prove that the Alexander polynomials of line arrangements Ᾱ C P² belonging to som

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Fantin, Silas. "Monodromia de curvas algébricas planas." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-10122007-165559/.

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Em 1968, J. Milnor introduziu a monodromia local de Picard-Lefschetz de uma hipersuperfície complexa com singularidade isolada. Em seguida, E. Brieskorn perguntou se esta monodromia é sempre finita. Em 1972, Lê Dúng Trâng provou que a resposta é positiva no caso de germes de curvas planas analíticas irredutíveis. Na época, já eram conhecidos exemplos de curvas planas com dois ramos e monodromia finita. Em 1973, N. A?Campo produziu o primeiro exemplo de germe de curva plana com dois ramos e monodromia infinita. Portanto, a questão mais simples, e ainda em aberto, que se coloca neste contexto, é

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Kahler, Stefan Alexander [Verfasser], Rupert [Akademischer Betreuer] [Gutachter] Lasser, Eberhard [Gutachter] Kaniuth, and Mourad [Gutachter] Ismail. "Characterizations of Orthogonal Polynomials and Harmonic Analysis on Polynomial Hypergroups / Stefan Alexander Kahler. Betreuer: Rupert Lasser. Gutachter: Eberhard Kaniuth ; Mourad Ismail ; Rupert Lasser." München : Universitätsbibliothek der TU München, 2016. http://d-nb.info/1105646483/34.

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Ishikawa, Katsumi. "Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links." Kyoto University, 2019. http://hdl.handle.net/2433/242574.

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Banks, Jessica E. "The Kakimizu complex of a link." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:d89d46a3-03f0-4a71-a746-8f024f988f63.

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We study Seifert surfaces for links, and in particular the Kakimizu complex MS(L) of a link L, which is a simplicial complex that records the structure of the set of taut Seifert surfaces for L. First we study a connection between the reduced Alexander polynomial of a link and the uniqueness of taut Seifert surfaces. Specifically, we reprove and extend a particular case of a result of Juhasz, using very different methods, showing that if a non-split homogeneous link has a reduced Alexander polynomial whose constant term has modulus at most 3 then the link has a unique incompressible Seifert su

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Book chapters on the topic "Alexander polynomial"

1

Lickorish, W. B. Raymond. "The Alexander Polynomial." In An Introduction to Knot Theory. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0691-0_6.

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Zieschang, Heiner. "On the Alexander and Jones Polynomial." In Topics in Knot Theory. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1695-4_12.

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Stoimenov, Alexander. "Hoste’s Conjecture and Roots of the Alexander Polynomial." In Knots, Low-Dimensional Topology and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16031-9_9.

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Ranicki, Andrew. "Alexander polynomials." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-12011-8_17.

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Kawauchi, Akio. "Multi-variable Alexander polynomials." In A Survey of Knot Theory. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9227-8_8.

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Murakami, Jun. "The multi-variable alexander polynomial and a one—parameter family of representations of U q (sl(2,C)) at q 2=−1." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0101201.

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Friedl, Stefan, and Stefano Vidussi. "A Survey of Twisted Alexander Polynomials." In The Mathematics of Knots. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15637-3_3.

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Kulikov, Vic S. "The Alexander Polynomials of Algebraic Curves in C 2." In Algebraic Geometry and its Applications. Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-99342-7_10.

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"Alexander polynomial, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/7531140927.

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Gilbert, N. D., and T. Porter. "Alexander matrices and Alexander polynomials." In Knots and Surfaces. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198533979.003.0008.

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Abstract Although the method that we have used to calculate the Alexander polynomial of a knot only uses the theory of determinants, the trouble with it is to know why it works. It is easy to check that the result is invariant under the Reidemeister moves but it would be nice to link it in with other invariants. ‘It would be nice’ sounds a weak reason, but often when one can do something by a different method, it is possible to see how to ‘squeeze’ the method a bit to get out more detailed information. What we will do is give a second method of calculating Alexander polynomials, this time usin

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Conference papers on the topic "Alexander polynomial"

1

ISHII, Atsushi. "SMOOTHING RESOLUTION FOR THE ALEXANDER–CONWAY POLYNOMIAL." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0007.

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Masbaum, Gregor. "Matrix-tree theorems and the Alexander–Conway polynomial." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2002. http://dx.doi.org/10.2140/gtm.2002.4.201.

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Hodorog, Madalina, Bernard Mourrain, and Josef Schicho. "A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity." In 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2010. http://dx.doi.org/10.1109/synasc.2010.41.

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OKA, M. "TANGENTIAL ALEXANDER POLYNOMIALS AND NON-REDUCED DEGENERATION." In Proceedings of the Trieste Singularity Summer School and Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706812_0023.

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Friedl, Stefan, and Stefano Vidussi. "Twisted Alexander polynomials, symplectic 4-manifolds and surfaces of minimal complexity." In Algebraic Topology - Old and New. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc85-0-3.

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Kitano, Teruaki, and Masaaki Suzuki. "Twisted Alexander polynomials and a partial order on the set of prime knots." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.307.

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