Homeomorphisms which are Dehn twists on the boundary

Details Homeomorphisms which are Dehn twists on the boundary Homeomorphisms which are Dehn twists on the boundary

2006-04-16

arxiv.org/abs/math/0604358v2

Algebr. Geom. Topol. 6 (2006) 1331-1340

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 20 September 2006

Scientific paper

10.2140/agt.2006.6.1331

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

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