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June 2019 Crystallographic Groups Arising from Teichmüller Spaces
Yukio MATSUMOTO
Tokyo J. Math. 42(1): 1-34 (June 2019). DOI: 10.3836/tjm/1502179302

Abstract

The purpose of this paper is to show that there is a natural connection between Teichmüller spaces and crystallographic groups. This connection was first discovered by the author when discussing the Deligne-Mumford compactification of moduli spaces (see \lq\lq {\it The Deligne-Mumford compactification and crystallographic groups}\rq\rq, preprint, 2018). In this paper, we will discuss the same connection from a slightly different viewpoint having in mind an analogy of the maximally degenerate frontier points of the augmented Teichmüller spaces and the cusp points of hyperbolic spaces.

Citation

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Yukio MATSUMOTO. "Crystallographic Groups Arising from Teichmüller Spaces." Tokyo J. Math. 42 (1) 1 - 34, June 2019. https://doi.org/10.3836/tjm/1502179302

Information

Published: June 2019
First available in Project Euclid: 18 July 2019

zbMATH: 07114898
MathSciNet: MR3982047
Digital Object Identifier: 10.3836/tjm/1502179302

Subjects:
Primary: 30F60
Secondary: 20H15

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 1 • June 2019
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