Spherical subcomplexes of spherical buildings

Abstract

Let B be a thick spherical building equipped with its natural CAT(1) metric and let M be a proper, convex subset of B. If M is open or if M is a closed ball of radius pi/2, then the maximal subcomplex supported by the complement of M is spherical and non contractible.

33 pages, 7 figures

References in corpus (1)

• Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem

Cited by in corpus (3)

• Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem
• Lipschitz connectivity and filling invariants in solvable groups and buildings
• Abels's groups revisited