Jamie B. Jorgensen
Published 2008-05-28Version 1
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.
A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody
Pseudo-Anosov dilatations and the Johnson filtration
Non-Roelcke precompactness of groups of surface homeomorphisms
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