Geometry & Topology

Spherical subcomplexes of spherical buildings

Bernd Schulz

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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 π2, then Λ, the maximal subcomplex supported by ΔM, 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

Keywords
spherical building Cohen–Macaulay connectivity

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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