Volume 6, issue 2 (2002)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Attaching handlebodies to 3–manifolds

Marc Lackenby

Geometry & Topology 6 (2002) 889–904

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 2000
Primary: 57N10
Secondary: 57N16, 57M50, 20F65
References
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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