Real reflections, commutators, and cross-ratios in complex hyperbolic space

Julien Paupert, Pierre Will

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We provide a concrete criterion to determine whether or not two given elements of PU.2; 1/ can bewritten as products of real reflections,with one reflection in common. As an application, we show that the Picardmodular groups PU(2, 1,Od)with d = 1, 2, 3, 7, 11 are generated by real reflections up to index 1, 2, 4 or 8.

Original languageEnglish (US)
Pages (from-to)311-352
Number of pages42
JournalGroups, Geometry, and Dynamics
Volume11
Issue number1
DOIs
StatePublished - 2017

Keywords

  • Complex hyperbolic geometry
  • Reflection groups

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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