## Geometry & Topology

### 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.

#### Article information

Source
Geom. Topol., Volume 6, Number 2 (2002), 889-904.

Dates
Revised: 20 December 2002
Accepted: 8 November 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882941

Digital Object Identifier
doi:10.2140/gt.2002.6.889

Mathematical Reviews number (MathSciNet)
MR1943384

Zentralblatt MATH identifier
1021.57010

#### Citation

Lackenby, Marc. Attaching handlebodies to 3–manifolds. Geom. Topol. 6 (2002), no. 2, 889--904. doi:10.2140/gt.2002.6.889. https://projecteuclid.org/euclid.gt/1513882941

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