Grid graphs and lattice surfaces

Details Grid graphs and lattice surfaces Grid graphs and lattice surfaces

2008-11-05

arxiv.org/abs/0811.0799v3

Mathematics

Dynamical Systems

This version includes a more detailed description of how to derive algebraic formulas for the surfaces using the Schwarz-Chris

Scientific paper

First, we apply Thurston's construction of pseudo-Anosov homeomorphisms to grid graphs and obtain translation surfaces whose Veech groups are commensurable to $(m,n,\infty)$ triangle groups. These surfaces were first discovered by Bouw and M\"oller, however our treatment of the surfaces differs. We construct these surfaces by gluing together polygons in two ways. We use these elementary descriptions to compute the Veech groups, resolve primitivity questions, and describe the surfaces algebraically. Second, we show that some $(m,n, \infty)$ triangle groups can not arise as Veech groups. This generalizes work of Hubert and Schmidt.

Affiliated with

Also associated with

No associations

Rating

Grid graphs and lattice surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Grid graphs and lattice surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Grid graphs and lattice surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-374270