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

Julien Paupert

doi:10.1016/j.top.2007.01.002

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

Julien Paupert

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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)
Pages (from-to)	155-183
Number of pages	29
Journal	Topology
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/j.top.2007.01.002
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

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10.1016/j.top.2007.01.002

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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.",

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N2 - 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.

AB - 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.

KW - Complex hyperbolic geometry

KW - Lattices in P U (2, 1)

KW - Momentum map

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

Abstract

Keywords

ASJC Scopus subject areas

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