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Jamie Jorgensen (Rice University)

### Title

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

Given a surface $\Sigma$ that bounds a handlebody $H$ and given a homeomorphism $f$ of $\Sigma$ the question of whether $f$ extends to a homeomorphism of $H$ is an important one. Finding homeomorphisms that do not extend to any handlebody bounding
$\Sigma$ is useful in various constructions (e.g. construction of knots that are not slice). We show that there are homeomorphisms that do not extend to any handlebody even with very strict algebraic constraints on the homeomorphism in the sense
that the homeomorphism may lie arbitrarily deep in the Johnson filtration of $\Sigma$.

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