Geodesic
The Homflypt skein module of a connected sum of 3–manifolds
Gilmer, Patrick M1 ; Zhong, Jianyuan K2
1Department of Mathematics, Louisiana State University, Baton Rouge LA 70803, USA
2Program of Mathematics and Statistics, Louisiana Tech University, Ruston LA 71272, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 605-625
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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.

DOI : 10.2140/agt.2001.1.605
Keywords: Young diagrams, relative skein module, Hecke algebra

Gilmer, Patrick M  1   ; Zhong, Jianyuan K  2

1 Department of Mathematics, Louisiana State University, Baton Rouge LA 70803, USA
2 Program of Mathematics and Statistics, Louisiana Tech University, Ruston LA 71272, USA 
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Gilmer, Patrick M; Zhong, Jianyuan K. The Homflypt skein module of a connected sum of 3–manifolds. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 605-625. doi: 10.2140/agt.2001.1.605

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