Surface Homeomorphisms That Do Not Extend to Any Handlebody and the Johnson Filtration

Details Surface Homeomorphisms That Do Not Extend to Any Handlebody and the Johnson Filtration Surface Homeomorphisms That Do Not Extend to Any Handlebody and the Johnson Filtration

2008-05-28

arxiv.org/abs/0805.4253v1

Mathematics

Geometric Topology

Scientific paper

We prove the existence of homeomorphisms of a closed, orientable surface of genus 3 or greater that do not extend to any handlebody bounded by the surface. We show that such homeomorphisms exist arbitrarily deep in the Johnson filtration of the mapping class group. The second and third terms of the Johnson filtration are the well-known Torelli group and Johnson subgroup, respectively. Richard Hain has obtained very similar results by different methods.

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