Algebraic & Geometric Topology

Homeomorphisms which are Dehn twists on the boundary

Darryl McCullough

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A homeomorphism of a 3–manifold M is said to be Dehn twists on the boundary when its restriction to M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in M. In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if M is compact, orientable, irreducible and M is a single torus, and M admits a homeomorphism which is a nontrivial Dehn twist on M, then M must be a solid torus.

Article information

Algebr. Geom. Topol., Volume 6, Number 3 (2006), 1331-1340.

Received: 31 August 2005
Revised: 6 July 2006
Accepted: 20 July 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M99: None of the above, but in this section
Secondary: 57R50: Diffeomorphisms

3–manifold boundary Dehn twist handlebody compression body


McCullough, Darryl. Homeomorphisms which are Dehn twists on the boundary. Algebr. Geom. Topol. 6 (2006), no. 3, 1331--1340. doi:10.2140/agt.2006.6.1331.

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