No Access

NEW INVARIANTS OF SIMPLE KNOTS

C. KEARTON

Mathematics Department, University of Durham, South Road, Durham DH1 3LE, England, United Kingdom

Search for more papers by this author

and

S. M. J. WILSON

Mathematics Department, University of Durham, South Road, Durham DH1 3LE, England, United Kingdom

Search for more papers by this author

https://doi.org/10.1142/S0218216508006166Cited by:0 (Source: Crossref)

Abstract

Our longterm plan is to classify knot modules and pairings by utilizing the power of computational number theory. The first step in this is to define invariants for which any given value arises from only finitely many modules: this is the purpose of the present paper.

Keywords:

AMSC: 57Q45, 57M25

References

E. Bayer-Fluckiger, C. Kearton and S. M. J. Wilson, J. Reine Angew. Math. 375, 167 (1987). Web of Science, Google Scholar
R. C. Blanchfield, Ann. Math. 65(2), 340 (1957). Crossref, Web of Science, Google Scholar
F. Châtelet, Les idéaux de l'anneau polynômes d'une variable à coefficients entiers, 1964, Algebraische Zahlentheorie (Mannheim), Ber. Tagung Math. Forschungsinst. Oberwolfach (Bibliographisches Institut Mannheim, 1966), pp. 43–51 . Google Scholar
R. H. Fox, Topology of 3-Manifolds and Related Topics (Englewood Cliffs, NJ), ed. M. K. Fort (Proc. Univ. of Georgia Inst., Prentice-Hall, 1962) pp. 120–167. Google Scholar
C. Kearton, Bull. Amer. Math. Soc. 79, 952 (1973), DOI: 10.1090/S0002-9904-1973-13274-4. Crossref, Web of Science, Google Scholar
C. Kearton, Trans. Amer. Math. Soc. 202, 141 (1975), DOI: 10.2307/1997303. Crossref, Web of Science, Google Scholar
C. Kearton, Knot Theory, Les Plans-sur-Bex, 1977, Lecture Notes in Mathematics 685, ed. J. C. Hausmann (Springer-Verlag, 1978) pp. 227–242. Crossref, Google Scholar
J. Levine, Trans. Amer. Math. Soc. 229, 1 (1977), DOI: 10.2307/1998498. Crossref, Web of Science, Google Scholar
J. P. Levine , Algebraic Structure of Knot Modules , Lecture Notes in Mathematics 772 ( Springer-Verlag , Berlin, Heidelberg, New York , 1980 ) . Crossref, Google Scholar
S. Naik and T. Stanford, J. Knot Theory Ramifications 12, 717 (2003), DOI: 10.1142/S0218216503002639. Link, Web of Science, Google Scholar
K. M. O'Brien, Seifert's algorithm, Châtelet bases and the Alexander ideals of classical knots, Ph.D. thesis, University of Durham (2002) . Google Scholar
H. F. Trotter, Invent. Math. 20, 173 (1973), DOI: 10.1007/BF01394094. Crossref, Web of Science, Google Scholar
H. F. Trotter, Knot Theory, Proceedings, Plans-sur-Bex 1977, Lecture Notes in Mathematics 685, ed. J.-C. Hausmann (Springer-Verlag, Berlin, Heidelberg, New York, 1978) pp. 291–299. Crossref, Google Scholar