The Homflypt skein module of a connected sum of 3-manifolds
arXiv:math/0012056 · doi:10.2140/agt.2001.1.605
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.
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-31.abs.html