No Access

ALEXANDER POLYNOMIALS OF RIBBON LINKS

JONATHAN A. HILLMAN

School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia

https://doi.org/10.1142/S0218216511008735Cited by:0 (Source: Crossref)

Abstract

We give a simple argument to show that every polynomial f(t) ∈ ℤ[t] such that f(1) = 1 is the Alexander polynomial of some ribbon 2-knot whose group is a 1-relator group, and we extend this result to links.

Keywords:

AMSC: 57Q45

References

I. R. Aitchison and D. S. Silver, Trans. Amer. Math. Soc. 306, 529 (1988), DOI: 10.1090/S0002-9947-1988-0933305-5. Crossref, Web of Science, Google Scholar
K. Asano and K. Yoshikawa, Pacific J. Math. 97, 267 (1981). Crossref, Web of Science, Google Scholar
M. S. Farber, Math. Ann. 293, 543 (1992), DOI: 10.1007/BF01444734. Crossref, Web of Science, Google Scholar
R. H. Fox and J. W. Milnor, Osaka J. Math. 3, 257 (1966). Web of Science, Google Scholar
S. Friedl, J. Knot Theory Ramifications 15, 601 (2006), DOI: 10.1142/S0218216506004622. Link, Web of Science, Google Scholar
J. A. Hillman , Algebraic Invariants of Links , Series on Knots and Everything 32 ( World Scientific Publishing Co , 2002 ) . Link, Google Scholar
A. Kawauchi, Osaka J. Math 15, 151 (1978). Web of Science, Google Scholar
S. Kinoshita, Ann. Math. 74, 518 (1961), DOI: 10.2307/1970296. Crossref, Web of Science, Google Scholar
J. Levine, Ann. Math. 84, 537 (1966), DOI: 10.2307/1970459. Crossref, Web of Science, Google Scholar
R. C. Lyndon, Ann. Math. 52, 650 (1950), DOI: 10.2307/1969440. Crossref, Web of Science, Google Scholar
Y. Nakagawa, Osaka J. Math. 15, 161 (1978). Web of Science, Google Scholar
V. Retakh, C. Reutenauer and A. Vaintrob, Differential Topology, Infinite-Dimensional Lie Algebras, and Applications, American Mathematical Society Translation Series 2 194 (American Mathematical Society, Providence, RI, 1999) pp. 237–246. Crossref, Google Scholar
D. Rolfsen , Knots and Links ( Publish or Perish, Inc , Berkeley, CA , 1976 ) . Google Scholar
H. Terasaka, Osaka J. Math. 11, 95 (1959). Google Scholar
K. Yoshikawa, Math. Sem. Notes Kobe Univ. 9, 241 (1981). Google Scholar