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(M1 connect sum M2) is isomorphic to S(M1) tensor S(M2) modulo torsion. In fact, we show that S(M1 connect sum M2) is isomorphic to S(M1) tensot 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.
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