#### 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.

Notes on file formats
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

AGT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**