Mapping class groupoids and Thompson's groups
A. Muhammed Uluda\u{g}, Mustafa Topkara, \"Ozge \"Ulkem, Ayberk Zeytin

TL;DR
This paper introduces new groupoids related to mapping class groups and Thompson's groups, exploring their connections to surface automorphisms and automorphisms of free groups.
Contribution
It defines the fundamental modular groupoid and a larger groupoid, establishing their relationships with surface mapping class groups, outer automorphisms of free groups, and Thompson's groups.
Findings
Defined the fundamental modular groupoid and its properties.
Established connections between the groupoids and Thompson's groups.
Explored the relationship with surface mapping class groups and automorphisms.
Abstract
We introduce a groupoid {\mathbf{\Pi MG}}}, called the fundamental modular groupoid, which is a variant of Penner's mapping class groupoid. We study how it relates to the surface mapping class groups and Thompson's group . We also introduce larger groupoid , which is related to outer automorphisms of free groups and Thompson's group in a similar manner.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Operator Algebra Research
