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

Patrick M. Gilmer; Jianyuan K. Zhong

doi:10.2140/agt.2001.1.605

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

Patrick M. Gilmer·Jianyuan K. Zhong

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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) tensot 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.

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BibTeX RIS

Patrick M. Gilmer, Jianyuan K. Zhong. 2000-12-08. The Homflypt skein module of a connected sum of 3-manifolds. https://doi.org/10.2140/agt.2001.1.605

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