Homeomorphisms which are Dehn twists on the boundary

McCullough, Darryl

doi:10.2140/agt.2006.6.1331

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Homeomorphisms which are Dehn twists on the boundary

Darryl McCullough

Algebraic & Geometric Topology 6 (2006) 1331–1340

DOI: 10.2140/agt.2006.6.1331

arXiv: math.GT/0604358

Abstract

A homeomorphism of a $3$ –manifold $M$ is said to be Dehn twists on the boundary when its restriction to $\partial M$ is isotopic to the identity on the complement of a collection of disjoint simple closed curves in $\partial M$ . 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 $\partial M$ is a single torus, and $M$ admits a homeomorphism which is a nontrivial Dehn twist on $\partial M$ , then $M$ must be a solid torus.

Keywords

3–manifold, boundary, Dehn twist, handlebody, compression body

Mathematical Subject Classification 2000

Primary: 57M99

Secondary: 57R50

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Publication

Received: 31 August 2005

Revised: 6 July 2006

Accepted: 20 July 2006

Published: 20 September 2006

Authors

Darryl McCullough
Department of Mathematics University of Oklahoma Norman, Oklahoma 73019 USA
http://www.math.ou.edu/~dmccullough/

Volume 6, issue 3 (2006)