Geometry & Topology

Attaching handlebodies to 3–manifolds

Marc Lackenby

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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

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

Received: 19 February 2002
Revised: 20 December 2002
Accepted: 8 November 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57N16: Geometric structures on manifolds [See also 57M50] 57M50: Geometric structures on low-dimensional manifolds 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

3–manifold handlebody word hyperbolic


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

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