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Vectorial metric compactification of symmetric spaces and affine buildings

Presented by: 
Anne Parreau Université de Grenoble
Wednesday 10th May 2017 - 09:00 to 10:00
INI Seminar Room 1
 In higher rank symmetric spaces and affine buildings, the natural
projection of segments in a closed Weyl chamber may be regarded as a
universal metric with vectorial values. It refines all Finsler
metrics.  Remarkably, many of the traditional basic properties of
CAT(0) spaces still hold for the vectorial metric, providing similar
properties for all Finsler metrics in a unified way.  We will show
that the classical Busemann compactification construction can be
directly conducted in this context, giving a natural compactification
by vector-valued horofunctions.  These functions correspond to
strongly asymptotic classes of facets.  This compactification is
naturally homeomorphic to the maximal Satake compactification and
dominates all linear Finsler compactifications.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons