Attaching handlebodies to 3–manifolds

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 2000

Primary: 57N10

Secondary: 57N16, 57M50, 20F65

References

Forward citations

Publication

Received: 19 February 2002

Revised: 20 December 2002

Accepted: 8 November 2002

Published: 21 December 2002

Proposed: Cameron Gordon

Seconded: Jean-Pierre Otal, Benson Farb

Authors

Marc Lackenby
Mathematical Institute Oxford University 24–29 St Giles’ Oxford OX1 3LB United Kingdom

Volume 6, issue 2 (2002)

Marc Lackenby