Geodesic
Homeomorphisms which are Dehn twists on the boundary
McCullough, Darryl1
1Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1331-1340
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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.

DOI : 10.2140/agt.2006.6.1331
Keywords: 3–manifold, boundary, Dehn twist, handlebody, compression body

McCullough, Darryl  1

1 Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA 
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McCullough, Darryl. Homeomorphisms which are Dehn twists on the boundary. Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1331-1340. doi: 10.2140/agt.2006.6.1331

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