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Twisted Alexander polynomial for the Braid group

Published online by Cambridge University Press:  17 April 2009

Takayuki Morifuji
Takayuki Morifuji
Affiliation:
Graduate School of Mathematical Sciences, The University of TokyoKomaba, Meguro, Tokyo 153–8914, Japan e-mail: [email protected]
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Abstract

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In this paper, we study the twisted Alexander polynomial, due to Wada [11], for the Jones representations [6] of Artin's braid group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 1 - 13
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bigelow, S., ‘The Burau representation is not faithful for n = 5’ Geom. Topol. 3 (1999), 397–404.Google Scholar
[2]Birman, J.Braids, links and mapping class groups, Annals of Math. Studies 82 (Princeton University Press, Princeton, NJ, 1974).Google Scholar
[3]Crowell, R.H. and Fox, R.H., Introduction to Knot theory (Ginn, Boston, 1963).Google Scholar
[4]Fox, R.H., ‘Free differential Calculus’, Ann. Of Math. 57 (1953), 547–560.Google Scholar
[5]Jiang, B. and Wang, S., ‘Twisted topological invariants associated with representations’, in Topics in Knot Theory, (Bozhüyük, M.E.. Editor) (Kluwer Academic Publishers, Dordrecht, 1993), pp. 211–227.Google Scholar
[6]Jones, V., ‘Hecke algebra representations of braid groups and link polynomials’, Ann, of Math. 126 (1987), 335–388.Google Scholar
[7]Kirk, P. and Livingston, C., ‘Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants’, Topology 38 (1999), 635–661.Google Scholar
[8]Kitano, T., ‘Twisted Alexander polynomial and Reidemeister torsion’, Pacific J. Math. 174 (1996), 431–442.CrossRefGoogle Scholar
[9]Lascoux, A. and Schutzenberger, M. P., ‘Polynomes de Kazhdan-Lusztig pour les grass-manniennes’, Astérisque 87–88 (1981), 249–266.Google Scholar
[10]Lin, X. S., ‘Representation of Knot groups and twisted Alexander polynomials’ (preprint).Google Scholar
[11]wada, M., ‘Twisted Alexander polynomial for finitely presentable groups’ Topology 33 (1994), 241–256.Google Scholar