Algebraic & Geometric Topology 1 (2001) 605–625

DOI: 10.2140/agt.2001.1.605

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

Primary: 57M25

References

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Publication

Received: 18 December 2000
Revised: 23 October 2001
Accepted: 24 October 2001
Published: 29 October 2001

Authors