Attaching handlebodies to 3-manifolds

Abstract

The main theorem of this paper is a generalisation of well known results about Dehn surgery to the case of attaching handlebodies to a simple 3-manifold. The existence of a finite set of `exceptional' curves on the boundary of the 3-manifold is established. Provided none of these curves is attached to the boundary of a disc in a handlebody, the resulting manifold is shown to be word hyperbolic and `hyperbolike'. We then give constructions of gluing maps satisfying this condition. These take the form of an arbitrary gluing map composed with powers of a suitable homeomorphism of the boundary of the handlebodies.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper26.abs.html

Cited by in corpus (2)

• Bounded combinatorics and uniform models for hyperbolic 3-manifolds
• Surface subgroups and handlebody attachment