Space of circle patterns on tori and its symplectic form
Geometric Topology
2024-06-12 v1 Complex Variables
Differential Geometry
Abstract
We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichm\"{u}ller space of a punctured surface. Via the embedding, the Weil-Petersson symplectic form is pulled back to the space of circle patterns. We investigate its non-degeneracy. On the other hand, we also complete a conjecture that the space of circle patterns is homeomorphic to the Teichm\"{u}ller space of the closed torus.
Cite
@article{arxiv.2406.06733,
title = {Space of circle patterns on tori and its symplectic form},
author = {Wai Yeung Lam},
journal= {arXiv preprint arXiv:2406.06733},
year = {2024}
}
Comments
14 pages. arXiv admin note: text overlap with arXiv:2404.17458