Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces

Details Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces

2010-12-08

arxiv.org/abs/1012.1699v1

Mathematics

Metric Geometry

77 pages

Scientific paper

The paper initiates a systematic study of Moebius structures and Ptolemy
spaces. We conjecture that every compact Ptolemy space with circles and many
space inversions is Moebius equivalent to the boundary at infinity of a rank
one symmetric space of noncompact type. We prove this conjecture for the class
of complex hyperbolic spaces as our main result.

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