Title: Towards an Instanton Floer Homology for Tangles

Abstract: In this thesis defense, I will motivate and study the problem of 
computing the cohomology rings of a class of moduli spaces of flat 
connections on orbifold Riemann surfaces. I will then discuss the parallel 
problem of computing the instanton Floer homology ring of a product link 
in product 3-manifold. Complete results in the case of genus 0 will be 
given. I will briefly discuss the application of these ideas to defining 
of instanton Floer homology for a tangle in a sutured 3-manifold. Emphasis 
will be on elementary ideas related to the moduli spaces rather than Floer 
homology.