On the Mapping class group of a genus 2 handlebody
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
TL;DR
This paper constructs a complex of incompressible surfaces in a genus 2 handlebody and uses its automorphisms to characterize the handlebody's mapping class group, showing all automorphisms are geometric.
Contribution
It introduces a new complex of incompressible surfaces and proves all automorphisms are induced by homeomorphisms, providing a novel characterization of the genus 2 handlebody's mapping class group.
Findings
Automorphisms of the complex are all geometric.
The complex contains the curve complex of the boundary as a subcomplex.
The approach characterizes the mapping class group via automorphisms.
Abstract
A complex of incompressible surfaces in a handlebody is constructed so that it contains, as a subcomplex, the complex of curves of the boundary of the handlebody. For genus 2 handlebodies, the group of automorphisms of this complex is used to characterize the mapping class group of the handlebody. In particular, it is shown that all automorphisms of the complex of incompressible surfaces are geometric, that is, induced by a homeomorphism of the handlebody.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation