The Homflypt skein module of a connected sum of 3–manifolds

If $M$ is an oriented $3$ –manifold, let $S (M)$ denote the Homflypt skein module of $M .$ We show that $S (M_{1} # M_{2})$ is isomorphic to $S (M_{1}) \otimes S (M_{2})$ modulo torsion. In fact, we show that $S (M_{1} # M_{2})$ is isomorphic to $S (M_{1}) \otimes S (M_{2})$ if we are working over a certain localized ring. We show the similar result holds for relative skein modules. If $M$ contains a separating $2$ –sphere, we give conditions under which certain relative skein modules of $M$ vanish over specified localized rings.

Keywords

Young diagrams, relative skein module, Hecke algebra

Mathematical Subject Classification 2000

Primary: 57M25

References

Forward citations

Publication

Received: 18 December 2000

Revised: 23 October 2001

Accepted: 24 October 2001

Published: 29 October 2001

Authors

Patrick M Gilmer
Department of Mathematics Louisiana State University Baton Rouge LA 70803 USA

Jianyuan K Zhong
Program of Mathematics and Statistics Louisiana Tech University Ruston LA 71272 USA

Volume 1, issue 1 (2001)

Patrick M Gilmer and Jianyuan K Zhong