Volume 17, issue 1 (2013)

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Spherical subcomplexes of spherical buildings

Bernd Schulz

Geometry & Topology 17 (2013) 531–562
Abstract

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

Keywords
spherical building, Cohen–Macaulay, connectivity
Primary: 51E24
Secondary: 11F75