## Geometry & Topology

### Spherical subcomplexes of spherical buildings

Bernd Schulz

#### 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 $dimΛ$–spherical and non-contractible.

#### Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 531-562.

Dates
Received: 22 August 2010
Accepted: 12 June 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732531

Digital Object Identifier
doi:10.2140/gt.2013.17.531

Mathematical Reviews number (MathSciNet)
MR3039769

Zentralblatt MATH identifier
1271.51006

Subjects
Primary: 51E24: Buildings and the geometry of diagrams
Secondary: 11F75: Cohomology of arithmetic groups

#### Citation

Schulz, Bernd. Spherical subcomplexes of spherical buildings. Geom. Topol. 17 (2013), no. 1, 531--562. doi:10.2140/gt.2013.17.531. https://projecteuclid.org/euclid.gt/1513732531

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