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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The Homflypt skein module of a connected sum of 3–manifolds

Patrick M Gilmer and Jianyuan K Zhong

Algebraic & Geometric Topology 1 (2001) 605–625

arXiv: math.GT/0012056

Abstract

If M is an oriented 3–manifold, let S(M) denote the Homflypt skein module of M. We show that S(M1#M2) is isomorphic to S(M1) S(M2) modulo torsion. In fact, we show that S(M1#M2) is isomorphic to S(M1) S(M2) 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
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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