Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T13:20:09.395Z Has data issue: false hasContentIssue false
  • English
  • Français

The Alexander module of a knotted theta-curve

Published online by Cambridge University Press:  24 October 2008

Rick Litherland
Rick Litherland
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

Let K be a knotted theta-curve with exterior X, and let ∂_X be one of the two pieces into which ∂X is divided by the meridians of the edges of K. Let X be the universal abelian cover of X. Then is a module over the group ring of H1(X); i.e. over . We call this the Alexander module of K, and denote it by A(K). This, rather than H1(X), seems to be the analogue of the Alexander module of a classical knot; it is a torsion module of deficiency 0. Moreover, it is not an invariant of X alone.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 95 - 106
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Hempel, John. Intersection calculus on surfaces with applications to 3-manifolds. Mem. Amer. Math. Roc. vol. 43. no. 282 (American Mathematical Society. 1983).Google Scholar
[2]Wolcott, Keith. The knotting of theta-curves and other graphs in S 3. Ph.D. thesis. University of Towa (1985).Google Scholar