Surface homeomorphisms that do not extend to any handlebody and the Johnson filtration
Jorgensen, Jamie Bradley
Cochran, Tim D.
Doctor of Philosophy
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.