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 language | English (US) |
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Pages (from-to) | 155-183 |
Number of pages | 29 |
Journal | Topology |
Volume | 46 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2007 |
Externally published | Yes |
Keywords
- Complex hyperbolic geometry
- Lattices in P U (2, 1)
- Momentum map
ASJC Scopus subject areas
- Geometry and Topology