Algebraic and Geometric Topology 1 (2001), paper no. 31, pages 605-625.

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

Patrick M. Gilmer, Jianyuan K. Zhong

Abstract. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M. We show that S(M_1 connect sum M_2) is isomorphic to S(M_1) tensor S(M_2) modulo torsion. In fact, we show that S(M_1 connect sum M_2) is isomorphic to S(M_1) tensor 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

AMS subject classification. Primary: 57M25.

DOI: 10.2140/agt.2001.1.605

Submitted: 18 December 2000. (Revised: 23 October 2001.) Accepted: 24 October 2001. Published: 29 October 2001.

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Patrick M. Gilmer, Jianyuan K. Zhong
Department of Mathematics, Louisiana State University
Baton Rouge, LA 70803, USA
and
Program of Mathematics and Statistics, Louisiana Tech University
Ruston, LA 71272, USA
Email: gilmer@math.lsu.edu, kzhong@coes.LaTech.edu

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