Volume 6, issue 3 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Homeomorphisms which are Dehn twists on the boundary

Darryl McCullough

Algebraic & Geometric Topology 6 (2006) 1331–1340

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 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.

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/