Reports@SCM, Vol 3, No 1 (2017)

Compactification of a diagonal action on the product of CAT (-1) spaces

Teresa García

Abstract


Let X be a proper, non-compact CAT(-1) space, and Γ a discrete cocompact subgroup of the isometries of X. We compactify the diagonal action of Γ on X x X considering a domain of the horofunction boundary with respect to the maximum metric.

Keywords: CAT (-1) space, group of isometries, compactication, horofunctions. MSC (2010): Primary: 55M25, 57P10. Secondary: 55P15, 57R19, 57N15.


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ISSN: 2385-4227 (electronic edition)