Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere

Irene Pasquinelli

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arXiv · 1509.05320

Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere

Irene Pasquinelli

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Abstract

Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy of hypergeometric functions. Later, Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for all lattices with three fold symmetry in Deligne-Mostow list. This is a generalisation of the works of Parker and Boadi and gives a different interpretation of the fundamental domain constructed by Deraux, Falbel and Paupert for some of these lattices.

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Irene Pasquinelli. 2015-09-17. Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere. https://arxiv.org/abs/1509.05320

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