Elliptic triangle groups in PU (2, 1), Lagrangian triples and momentum maps

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Abstract

We determine the possible eigenvalues of elliptic matrices A, B, C in P U (2, 1) satisfying A B C = 1. This is done by describing geometrically the image of a group-valued momentum map for the (non-compact) group action of P U (2, 1) by conjugation on C1 × C2 where C1 and C2 are fixed elliptic conjugacy classes in P U (2, 1). Contrary to the compact case, this image is not always convex; rather it is the union of one, two or three convex polygons in T2 / S2. The main motivation was to analyze elliptic triangle groups in P U (2, 1) such as Mostow's lattices.

Original languageEnglish (US)
Pages (from-to)155-183
Number of pages29
JournalTopology
Volume46
Issue number2
DOIs
StatePublished - Mar 1 2007

Keywords

  • Complex hyperbolic geometry
  • Lattices in P U (2, 1)
  • Momentum map

ASJC Scopus subject areas

  • Geometry and Topology

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