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ALEXANDER–LIN TWISTED POLYNOMIALS

DANIEL S. SILVER

Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA

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and

SUSAN G. WILLIAMS

Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA

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https://doi.org/10.1142/S0218216511008838Cited by:3 (Source: Crossref)

Abstract

Lin's definition of twisted Alexander knot polynomial is extended for finitely presented groups. Cha's fibering obstruction theorem is generalized. The group of the 2-twist-spun trefoil knot is seen to have a faithful representation that yields a trivial twisted Alexander polynomial.

Keywords:

AMSC: 57M25

References

J. S. Birman, Proc. Amer. Math. Soc. 41, 634 (1973), DOI: 10.1090/S0002-9939-1973-0330295-8. Crossref, Web of Science, Google Scholar
J. Cha, Trans. Amer. Math. Soc. 355, 4187 (2003), DOI: 10.1090/S0002-9947-03-03348-8. Crossref, Web of Science, Google Scholar
S. Friedl, private communication . Google Scholar
S. Friedl and T. Kim, Topology 45, 929 (2006). Crossref, Web of Science, Google Scholar
S. Friedl and S. Vidussi, A survey of twisted Alexander polynomials, preprint (2009) . Google Scholar
H. Goda, T. Kitano and T. Morifuji, Comment. Math. Helv. 80, 51 (2005). Web of Science, Google Scholar
L. H. Kauffman, Atti Sem. Mat. Fis. Univ. Modena IL, 241 (2001). Google Scholar
L. H. Kauffman, A survey of virtual knot theory, Knots in Hellas '98 (Delphi)24, Series on Knots and Everything (World Scientific Publishing, River Edge, NJ, 2000) pp. 143–202. Google Scholar
P. Kirk and C. Livingston, Topology 38, 635 (1999). Crossref, Web of Science, Google Scholar
T. Kitano, Pacific J. Math. 174, 431 (1996). Crossref, Web of Science, Google Scholar
T. Kitano and T. Morifuji, Ann. Sc. Norm. Super. Pisa Cl. Sci. 4, 179 (2005). Google Scholar
T. Kitano, M. Suzuki and M. Wada, Algebr. Geom. Topol. 5, 1315 (2005), DOI: 10.2140/agt.2005.5.1315. Crossref, Web of Science, Google Scholar
T. Kitayama, Normalization of twisted Alexander invariants, preprint (2008) . Google Scholar
D. H. Kochloukova, Comment. Math. Helv. 81, 931 (2006). Web of Science, Google Scholar
X. S. Lin, Acta Math. Sinica 17, 361 (2001), DOI: 10.1007/s101140100122. Crossref, Web of Science, Google Scholar
R. C. Lyndon and P. E. Schupp , Combinatorial Group Theory ( Springer-Verlag , Berlin , 1977 ) . Crossref, Google Scholar
A. Pajitnov, St. Petersburg Math. J. 18, 809 (2007), DOI: 10.1090/S1061-0022-07-00975-2. Crossref, Google Scholar
D. S. Silver, Math. Ann. 296, 585 (1993), DOI: 10.1007/BF01445122. Crossref, Web of Science, Google Scholar
D. S. Silver and W. Whitten, J. Knot Theory Ramifications 15, 153 (2006). Link, Web of Science, Google Scholar
E. R. Strasser, Knot-like groups, in Knots, Groups, and 3-Manifolds (papers dedicated to the memory of R. H. Fox), Annals of Mathematics Studies, Vol. 84 (Princeton University Press, Princeton, N. J., 1975), pp. 119–133 . Google Scholar
M. Suzuki, Bull. Austral. Math. Soc. 70, 67 (2004), DOI: 10.1017/S0004972700035826. Crossref, Web of Science, Google Scholar
M. Wada, Topology 33, 241 (1994), DOI: 10.1016/0040-9383(94)90013-2. Crossref, Web of Science, Google Scholar
E. C. Zeeman, Trans. Amer. Math. Soc. 115, 471 (1965), DOI: 10.1090/S0002-9947-1965-0195085-8. Crossref, Web of Science, Google Scholar