Geometry & Topology, Vol. 6 (2002)
Paper no. 26, pages 889--904.
Attaching handlebodies to 3-manifolds
Marc Lackenby
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
AMS subject classification.
Primary: 57N10.
Secondary: 57N16, 57M50, 20F65.
DOI: 10.2140/gt.2002.6.889
E-print: arXiv:math.GT/0109059
Submitted to GT on 19 February 2002.
(Revised 20 December 2002.)
Paper accepted 08 November 2002.
Paper published 21 December 2002.
Notes on file formats
Marc Lackenby
Mathematical Institute, Oxford University
24-29 St Giles', Oxford OX1 3LB, UK
Email: lackenby@maths.ox.ac.uk
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