Natasa Macura

CAT(0) spaces with polynomial divergence of geodescis

Abstract:
We will describe examples of non-positively curved spaces with
polynomial divergence of geodesics of degree greater than two,
answering a question of Gersten if such CAT(0) complexes exist.
Gersten posed this question after constructing a CAT(0) 2-complex
with quadratic divergence and therefore showing that the expectation,
which he attributes to Gromov, that geodesics diverge either
linearly or exponentially in non-positively curved spaces fails
for CAT(0) complexes. We construct a family of finite 2-dimensional
cube complexes whose universal covers are CAT(0) and have
the polynomial divergence of geodesics of desired degree.