Geometry & Topology 6 (2002) 889–904

DOI: 10.2140/gt.2002.6.889

arXiv: math.GT/0109059

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.

Keywords

3–manifold, handlebody, word hyperbolic

Mathematical Subject Classification

Primary: 57N10

Secondary: 20F65, 57M50, 57N16

References

Forward citations

Publication

Received: 19 February 2002
Revised: 20 December 2002
Accepted: 08 November 2002
Published: 21 December 2002
Proposed: Cameron Gordon
Seconded: Jean-Pierre Otal, Benson Farb

Authors