Spherical subcomplexes of spherical buildings

Schulz, Bernd

doi:10.2140/gt.2013.17.531

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Spherical subcomplexes of spherical buildings

Bernd Schulz

Geometry & Topology 17 (2013) 531–562

DOI: 10.2140/gt.2013.17.531

Abstract

Let $Δ$ be a thick, spherical building equipped with its natural CAT(1) metric and let $M$ be a proper, convex subset of $Δ$ . If $M$ is open or if $M$ is a closed ball of radius $π ∕ 2$ , then $Λ$ , the maximal subcomplex supported by $Δ ∖ M$ , is $dim Λ$ –spherical and non-contractible.

Keywords

spherical building, Cohen–Macaulay, connectivity

Mathematical Subject Classification 2000

Primary: 51E24

Secondary: 11F75

References

Publication

Received: 22 August 2010

Accepted: 12 June 2012

Published: 5 April 2013

Proposed: Martin R Bridson

Seconded: Walter Neumann, Jean-Pierre Otal

Authors

Bernd Schulz
Tulpenhofstraße 31 63067 Offenbach Germany

Volume 17, issue 1 (2013)