COMBINATORIAL METHODS IN DEHN SURGERY

CAMERON MCA. GORDON

Abstract. This is an expository paper, in which we give a summary of some of the joint work of John Luecke and the author on Dehn surgery. We consider the situation where we have two Dehn fillings M(α) and M(β) on a given 3-manifold M, each containing a surface that is either essential or a Heegaard surface. We show how a combinatorial analysis of the graphs of intersection of the two corresponding punctured surfaces in M enables one to find faces of these graphs which give useful topological information about M(α) and M(β), and hence, in certain cases, good upper bounds on the intersection number Δ(α, β) of the two filling slopes.