## Algebraic & Geometric Topology

### Homeomorphisms which are Dehn twists on the boundary

Darryl McCullough

#### 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796580

Digital Object Identifier
doi:10.2140/agt.2006.6.1331

Mathematical Reviews number (MathSciNet)
MR2253449

Zentralblatt MATH identifier
1135.57011

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796580

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