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G&T Monographs |
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Essential curves in handlebodies and topological
contractions
Viatcheslav Grines and François Laudenbach
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Geometry & Topology 12 (2008)
981–985
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Abstract
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If X is a compact set, a topological contraction is a
self-embedding f such that the intersection of the successive images
fk(X), k > 0, consists of one point. In dimension 3, we
prove that there are smooth topological contractions of the
handlebodies of genus ≥ 2 whose image is essential.
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Keywords
Heegaard splitting, compression disk,
North-South diffeomorphism
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Mathematical Subject Classification
Primary: 57M25
Secondary: 37D15
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Publication
Received: 13 November 2007
Accepted: 8 February 2008
Published: 12 May 2008
Proposed: Cameron Gordon
Seconded: Martin Bridson, Walter Neumann
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