Veech groups of flat surfaces with poles

2016/06/12 by Tahar, Guillaume
#30F30 #32G15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1606.03706

Abstract

Flat surfaces that correspond to meromorphic 1-forms or to meromorphic quadratic differentials containing poles of order two and higher are surfaces of infinite area. We classify groups that appear as Veech groups of translation surfaces with poles. We characterize those surfaces such that their GL⁺(2,ℝ)-orbit or their SL(2,ℝ)-orbit is closed. Finally, we provide a way to determine the Veech group for a typical infinite surface in a given chamber of a stratum.

Related

• Veech groups of flat structures on Riemann surfaces
• Translation Surfaces With Finite Veech Groups
• On the Ends of groups and the Veech groups of infinite-genus surfaces
• Cyclic hyperbolic Veech groups in finite area
• Totally non congruence Veech groups