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Essential curves in handlebodies and topological contractions

Viatcheslav Grines and François Laudenbach

Geometry & Topology 12 (2008) 981–985

DOI: 10.2140/gt.2008.12.981
Abstract

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.

Keywords

Heegaard splitting, compression disk, North-South diffeomorphism
Mathematical Subject Classification

Primary: 57M25

Secondary: 37D15
References
Publication

Received: 13 November 2007
Accepted: 8 February 2008
Published: 12 May 2008
Proposed: Cameron Gordon
Seconded: Martin Bridson, Walter Neumann
Authors
Viatcheslav Grines
N. Novgorod State University
Gagarina 23
N. Novgorod
603950 Russia
François Laudenbach
Laboratoire de mathématiques Jean Leray
UMR 6629 du CNRS
Faculté des Sciences et Techniques
Université de Nantes
2, rue de la Houssinière
F-44322 Nantes cedex 3
France