|
Alexander polynomials of equivariant slice and ribbon knots in 
Authors:
James F. Davis and Swatee Naik
Journal:
Trans. Amer. Math. Soc. 358 (2006), 2949-2964
MSC (2000):
Primary 57M25
Posted:
May 26, 2005
MathSciNet review:
2216254
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: This paper gives an algebraic characterization of Alexander polynomials of equivariant ribbon knots and a factorization condition satisfied by Alexander polynomials of equivariant slice knots.
References
- 1.
I. Aitchison and D. Silver, On certain fibred ribbon disc pairs, Trans. Amer. Math. Soc. 306 (1988) 529-550. MR 0933305 (89f:57004)
- 2.
G. Burde and H. Zieschang, Knots, Studies in Math. 5, de Gruyter, 1985.MR 0808776 (87b:57004)
- 3.
J. C. Cha and K. H. Ko, On equivariant slice knots, Proc. Amer. Math. Soc. 127 (1999) 2175-2182. MR 1605928 (2000a:57006)
- 4.
J. C. Cha, A characterization of the Murasugi polynomial of an equivariant slice knot, (2004) preprint.
- 5.
J. Conway, An enumeration of knots and links and some of their algebraic properties in Computational Problems in Abstract Algebra, Proc. Conf. Oxford 1967, 329-358 (ed. John Leech) Pergamon Press, 1970. MR 0258014 (41:2661)
- 6.
J. F. Davis and C. Livingston, Alexander polynomials of periodic knots, Topology 30 (1991) 551-564. MR 1133872 (92k:57008)
- 7.
C. H. Giffen, The generalized Smith conjecture, Amer. J. Math. 88 (1966) 187-198. MR 0198462 (33:6620)
- 8.
R. H. Fox, A quick trip through knot theory, in Topology of 3-Manifolds and Related Topics (Proc. The Univ. of Georgia Institute, 1961), 120-167, (ed. M.K. Fort) Prentice Hall, 1962. MR 0140099 (25:3522)
- 9.
R. H. Fox, Some problems in knot theory, in Topology of 3-Manifolds and Related Topics (Proc. The Univ. of Georgia Institute, 1961), 168-176, (ed. M.K. Fort) Prentice Hall, 1962. MR 0140100 (25:3523)
- 10.
R. H. Fox and J. W. Milnor, Singularities of 2-spheres in 4-space and cobordism of knots, Osaka J. Math. 3 (1966) 257-267. MR 0211392 (35:2273)
- 11.
R. E. Gompf and A. I. Stipsicz, 4-manifolds and Kirby Calculus, Amer. Math. Soc., 1999. MR 1707327 (2000h:57038)
- 12.
J. A. Hillman, Polynomials of equivariantly slice knots, (2003) preprint.
- 13.
R. Kirby, Problems in low dimensional topology, in Geometric Topology (Athens, GA, 1993), 35-473, ed. R. Kirby, Amer. Math. Soc., 1997. MR 1470751
- 14.
A. A. Kosinski, Differential Manifolds, Academic Press, 1993.MR 1190010 (95b:57001)
- 15.
K. H. Ko, D. H. Choi, and W. T. Song, Seifert matrices and equivariant concordances of periodic knots, (1997) preprint.
- 16.
J. Levine, A characterization of knot polynomials, Topology 4 (1965) 135-141. MR 0180964 (31:5194)
- 17.
J. Milnor, A duality theorem for Reidemeister torsion, Ann. of Math. (2) 76 (1962) 137-147. MR 0141115 (25:4526)
- 18.
J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358-426. MR 0196736 (33:4922)
- 19.
J. Morgan and H. Bass, ed., The Smith Conjecture, Academic Press, 1984. MR 0758459 (86i:57002)
- 20.
K. Murasugi, On periodic knots, Comment. Math. Helv. 46 (1971) 162-174.MR 0292060 (45:1148)
- 21.
S. Naik, Equivariant slice knots in
 , Knots `96 (Tokyo), 81-89, Proceedings of the Fifth International Research Institute of Mathematical Society of Japan, held at Waseda University, Tokyo, July 22-26, 1996, ed. S. Suzuki, World Sci. Publishing, 1997.MR 1664952 (99k:57028)
- 22.
D. S. Rim, Modules over finite groups, Ann. of Math. (2) 69 (1959) 700-712.MR 0104721 (21:3474)
- 23.
D. Rolfsen, Knots and Links, Mathematics Lecture Series, No. 7. Publish or Perish, Inc., 1976.MR 0515288 (58:24236)
- 24.
P. A. Smith, Transformations of finite period, Ann. of Math. (2) 39 (1938) 127-164. MR 1503393
- 25.
J. R. Smith, Acyclic localizations, J. Pure Appl. Algebra 12 (1978) 117-127. MR 0491895 (58:11075)
- 26.
H. Terasaka On null equivalent knots, Osaka Math. J. 11 (1959) 95-113. MR 0117736 (22:8511)
- 27.
V. G. Turaev, Reidemeister torsion in knot theory, Russian Math. Surveys 41 (1986) 119-182. MR 0832411 (87i:57009)
- 28.
C. T. C. Wall, Surgery on Compact Manifolds, Academic Press, 1970.MR 0431216 (55:4217)
- 29.
G. W. Whitehead, Elements of Homotopy Theory, Springer, 1978.MR 0516508 (80b:55001)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC (2000):
57M25
Retrieve articles in all journals
with MSC (2000):
57M25
Additional Information
James F. Davis
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405-4301
Swatee Naik
Affiliation:
Department of Mathematics & Statistics, University of Nevada, Reno, Nevada 89557
DOI:
http://dx.doi.org/10.1090/S0002-9947-05-03741-4
PII:
S 0002-9947(05)03741-4
Received by editor(s):
May 20, 2002
Received by editor(s) in revised form:
May 11, 2004
Posted:
May 26, 2005
Additional Notes:
The first author was partially supported by a grant from the National Science Foundation
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
|
