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

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