#### Volume 6, issue 3 (2006)

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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 $\partial M$ 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
Primary: 57M99
Secondary: 57R50