Tokyo Journal of Mathematics

Crystallographic Groups Arising from Teichmüller Spaces


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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.

Article information

Tokyo J. Math., Volume 42, Number 1 (2019), 1-34.

First available in Project Euclid: 18 July 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30F60: Teichmüller theory [See also 32G15]
Secondary: 20H15: Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]


MATSUMOTO, Yukio. Crystallographic Groups Arising from Teichmüller Spaces. Tokyo J. Math. 42 (2019), no. 1, 1--34.

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