A Mayer-Vietoris Theorem for the Kauffman Bracket Skein Module

Abstract

The nth relative Kauffman bracket skein modules are defined and two theorems are given relating them to the Kauffman bracket skein module of a 3-manifold. The first theorem covers the case when the 3-manifold is split along a separating closed orientable surface and the second theorem addresses the case when the surface is nonseparating.