Combinatorial models for surface and free group symmetries

The curve complex of Harvey allows combinatorial representation of a surface mapping class group by describing its action on simple closed curves. Similar complexes of spheres, free factors, and free splittings allow combinatorial representation of the automorphisms of a free group. We consider a Birman exact sequence for combinatorial models of mapping class groups and free group automorphisms. We apply this and other extension techniques to compute the automorphism groups of several simplicial complexes associated with mapping class groups and automorphisms of free groups.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Scott, Shane

Advisor dc:contributor.advisor

• Margalit, Dan

Committee members dc:contributor.committeemember

• Brendle, Tara
• Etnyre, John
• Hom, Jen
• Wickelgren, Kirsten

• Geometric group theory
• Geometry
• Topology
• Surfaces
• Mapping classes
• Curve graph
• Curve complex

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1853/60722

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/60722