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

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

2000-12-08

arxiv.org/abs/math/0012056v2

Algebr. Geom. Topol. 1 (2001) 605-625

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-31.abs.html

Scientific paper

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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