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

@article{Gilmer2000TheHS,
title={The Homflypt skein module of a connected sum of 3-manifolds},
author={Patrick M. Gilmer and Jianyuan K. Zhong},
journal={Algebraic \& Geometric Topology},
year={2000},
volume={1},
pages={605-625}
}
• Published 8 December 2000
• Mathematics
• Algebraic & Geometric Topology
If M is an oriented 3-manifold, let S(M )d enote the Homf lypt skein module of M: We show that S (M 1#M 2) 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 specied localized rings.
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