Essential curves in handlebodies and topological contractions

Details Essential curves in handlebodies and topological contractions Essential curves in handlebodies and topological contractions

2007-10-02

arxiv.org/abs/0710.0516v1

Geometry & Topology 12 (2008) 981-986

Mathematics

Geometric Topology

Scientific paper

If $X$ is a compact set, a {\it 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. Our proof is based on an easy criterion for a simple curve to be essential in a handlebody.

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