A homeomorphism of a –manifold is said to be Dehn twists on the boundary when its restriction to is isotopic to the identity on the complement of a collection of disjoint simple closed curves in . In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if is compact, orientable, irreducible and is a single torus, and admits a homeomorphism which is a nontrivial Dehn twist on , then must be a solid torus.
"Homeomorphisms which are Dehn twists on the boundary." Algebr. Geom. Topol. 6 (3) 1331 - 1340, 2006. https://doi.org/10.2140/agt.2006.6.1331