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

2008/05/28 by Jamie Bradley Jorgensen, Jorgensen, Jamie B.
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.0805.4253

openalex publication_date 2008/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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