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A note on degrees of twisted Alexander polynomials II

Takayuki Morifuji|Masaaki Suzuki
대한수학회 (The Korean Mathematical Society)|2013.05|대한수학회보 (Bulletin of the KMS)|제50권 제3호|pp. 929-934

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키워드

knot grouptwisted Alexander polynomialzero-surgery
주제분류수학

초록

In this short note we discuss degrees of twisted Alexander polynomials and demonstrate an explicit example of a closed 3-manifold which is related to the degree formula due to Friedl, Kim and Kitayama.

Abstract

In this short note we discuss degrees of twisted Alexander polynomials and demonstrate an explicit example of a closed 3-manifold which is related to the degree formula due to Friedl, Kim and Kitayama.

참고문헌 (12)

  1. S. Friedl, "Poincare duality and degrees of twisted Alexander polynomials", Indiana Univ. Math. J
  2. S. Friedl, "A survey of twisted Alexander polynomials, The Mathematics of Knots: Theory and Application (Contributions in Mathematical and Computational Sciences)", pp.45~94 (2010), Markus Banagl and Denis Vogel
  3. T. Kim, "Twisted Alexander polynomials and character varieties of 2- bridge knot groups", Internat. J. Math, 23, pp.18~ (2012)
  4. T. Kitano, "Twisted Alexander polynomial and Reidemeister torsion", Pacific J. Math, 174(2), pp.431~442 (1996)
  5. T. Kitano, "Divisibility of twisted Alexander polynomials and fibered knots", Ann. Sc. Norm. Super. Pisa Cl. Sci, 4(1), pp.179~186 (2005)
  6. T. Kitano, "On the number of SL(2; Z", pZ)-representations of knot groups, 2012, pp.21(1), 18~
  7. X. S. Lin, "Representations of knot groups and twisted Alexander polynomials", Acta Math. Sin, 17(3), pp.361~380 (2001)
  8. J. Milnor, "Whitehead torsion", Bull. Amer. Math. Soc, 72, pp.358~426 (1966)
  9. T. Morifuji, "Twisted Alexander polynomials of twist knots for nonabelian representations", Bull. Sci. Math, 132(5), pp.439~453 (2008)
  10. T. Morifuji, "A note on degrees of twisted Alexander polynomials", RIMS Kokyuroku, 1747, pp.121~125 (2011)
  11. R. Riley, "Nonabelian representations of 2-bridge knot groups, Quart", J. Math. Oxford Ser, 34, pp.191~208 (1984)
  12. M. Wada, "Twisted Alexander polynomial for finitely presentable groups", Topology, 33(2), pp.241~256 (1994)

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