Topological median algebra structures on ER homology manifolds I: local cubulation
Authors
Mladen Bestvina
Kenneth Bromberg
Michah Sageev
Abstract
We study topological median algebra structures on Euclidean spaces
and, more generally, ER homology manifolds. We show that all such
median structures have a local CAT(0) cubulation structure. We also
show that topological median algebra structures are completely metrizable as
median metric spaces if and only if intervals are compact. We give
examples of both metrizable and non-metrizable such structures, as
well as provide a construction for producing many non-locally
cubulated topological median algebra structures on the unit ball in
Euclidean space.
