Finiteness conjecture for 3-manifolds obtained from handlebodies by attaching 2-handles

Abstract

We study a generalized Witten's finiteness conjecture for the skein modules of oriented compact 3-manifolds with boundary. We formulate an equivalent version of the generalized finiteness conjecture using handlebodies and 2-handles, and prove the conjecture for some classes with the handlebodies of genus 2 and 3 using the equivalent version.

arXiv comment21 pages, 13 figures, Added an example in Theorem 2.13 and Appendix A