Finiteness conditions on translation surfaces
Joshua P. Bowman
TL;DR
This paper investigates different notions of finiteness on translation surfaces and establishes conditions under which the Veech group is discrete, particularly relating to finite area or total boundedness.
Contribution
It provides new criteria linking finiteness properties of translation surfaces to the discreteness of their Veech groups.
Findings
Veech group is discrete if the surface has finite area
Veech group is discrete if the surface is totally bounded
Various metric and analytic finiteness notions are analyzed
Abstract
We consider various metric and analytic notions of finiteness on translation surfaces. The Veech group of a surface is discrete if the surface has finite area or is totally bounded.
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
TopicsHolomorphic and Operator Theory · Advanced Topology and Set Theory · advanced mathematical theories