Equivariant Morse theory on Vietoris-Rips complexes & universal spaces for proper actions

Abstract

We formalize an equivariant version of Bestvina-Brady discrete Morse theory, and apply it to Vietoris-Rips complexes in order to exhibit finite universal spaces for proper actions for all asymptotically CAT(0) groups.

Final revision, to appear in Bulletin of the London Mathematical Society. Minor changes, correcting some inconsequential mistakes and improving the exposition, based on a thorough referee report. 18 pages

References in corpus (3)

• Algebraic K-theory of group rings and the cyclotomic trace map
• Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods
• Stable finiteness properties of infinite discrete groups

Cited by in corpus (1)

• Contractibility of the Rips complexes of Integer lattices via local domination