#### Volume 12, issue 2 (2008)

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Essential curves in handlebodies and topological contractions

### Viatcheslav Grines and François Laudenbach

Geometry & Topology 12 (2008) 981–985
##### Abstract

If $X$ is a compact set, a topological contraction is a self-embedding $f$ such that the intersection of the successive images ${f}^{k}\left(X\right)$, $k>0$, consists of one point. In dimension 3, we prove that there are smooth topological contractions of the handlebodies of genus $\ge 2$ whose image is essential.

##### Keywords
Heegaard splitting, compression disk, North-South diffeomorphism
Primary: 57M25
Secondary: 37D15