Heegaard structures of negatively curved 3-manifolds

Abstract

Let M be an orientable complete hyperbolic 3-manifold of finite volume and with d ordered cusps ci,... , c^. Denote by M the collection of all manifolds obtained by Dehn surgery on M i.e., if q Q d , q = (gi,... , qd), let M q denote the manifold obtained by qi surgery on the i-th. cusp, i = 1,... ,d, with respect to some prechosen basis for the cuspital homology. Note that topologically M is contained in M q for all q. By a Heegaard splitting for M we mean a decomposition of M into two compression bodies as in [CG].