Essential curves in handlebodies and topological contractions

Grines, Viatcheslav; Laudenbach, François

doi:10.2140/gt.2008.12.981

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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 $f^{k} (X)$ , $k > 0$ , consists of one point. In dimension 3, we prove that there are smooth topological contractions of the handlebodies of genus $\geq 2$ whose image is essential.

Keywords

Heegaard splitting, compression disk, North-South diffeomorphism

Mathematical Subject Classification 2000

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

Volume 12, issue 2 (2008)