Geometry & Topology, Vol. 6 (2002)
Paper no. 26, pages 889--904.
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
3-manifold, handlebody, word hyperbolic
AMS subject classification.
Secondary: 57N16, 57M50, 20F65.
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
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