Reidemeister torsion of link complements in a 3-torus
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 11-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the Reidemeister torsion and the twisted Alexander polynomial of the complement of a link in a three-dimensional torus are the same.
Keywords: knots, links, three-dimensional torus, twisted Alexander polynomial, $CW$-complex
Mots-clés : Reidemeister torsion, Fox calculus.
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Bao Vuong. Reidemeister torsion of link complements in a 3-torus. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 87 (2024), pp. 11-21. http://geodesic.mathdoc.fr/item/VTGU_2024_87_a1/

[1] Vuong B., Fundamental group and twisted Alexander polynomial of knots in 3-torus, arXiv: (submitted) 2302.10461

[2] Milnor J., “A duality theorem for Reidemeister torsion”, Annals of Mathematics, 76:2 (1962), 137–147 | DOI | MR | Zbl

[3] Seifert H., “Uber das Geschlecht von Knoten”, Mathematische Annalen, 110 (1934), 571–592 | DOI | MR

[4] Huynh V.Q., Le T.T.Q., “Twisted Alexander polynomial of links in the projec tive space”, Journal of Knot Theory and Its Ramifications, 17 (2008), 411–438 | DOI | MR | Zbl

[5] Cattabriga A., Manfredi E., Mulazzani M., “On knots and links in lens spaces”, Topology and Its Applications, 160 (2013), 430–442 | DOI | MR | Zbl

[6] Fox R. H., “A quick trip through knot theory”, Topology of 3-Manifolds, ed. M.K. Fort, Jr., Prentice-Hall, Englewood Cliffs, N. J., 1962 | MR

[7] Wada M., “Twisted Alexander polynomial for finitely presentable groups”, Topology, 33:2 (1994), 241–256 | DOI | MR | Zbl

[8] Horvat E., Bostjan Gabrovsek, “The Alexander polynomial of links in lens spaces”, Journal of Knot Theory and Its Ramifications, 28:8 (2019), 1950049 | DOI | MR | Zbl

[9] Turaev V., Torsion of 3-Dimensional Manifolds, Birkhauser Verlag, Basel, 2002 | MR

[10] Turaev V., Introduction to Combinatorial Torsions, Lectures in Mathematics ETHZurich, Birkhauser Verlag, Basel, 2001 | MR | Zbl

[11] Milnor J., “Whitehead torsion”, Bulletin of the American Mathematical Society, 72 (1966), 358–426 | DOI | MR | Zbl

[12] Whitehead J.H.C., “Simple homotopy types”, American Journal of Mathematics, 72 (1950), 1–57 | DOI | MR | Zbl

[13] Fox R.H., “Free differential calculus I”, Annals of Mathematics, 57 (1953), 547560 | DOI | MR

[14] Fox R.H., “Free differential calculus II”, Annals of Mathematics, 59 (1954), 196210 | DOI | MR

[15] Lickorish W.B.R., An Introduction to Knot Theory, Graduate Texts in Mathematics, 175, Springer, 1997 | DOI | MR | Zbl

[16] Kitano T., “Twisted Alexander polynomial and Reidemeister torsion”, Pacific Journal of Mathematics, 174:2 (1996), 431–442 | DOI | MR | Zbl

[17] Kirk P., Livingston C., “Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants”, Topology, 38:3 (1999), 635–661 | DOI | MR | Zbl