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CAT(0) spaces with polynomial divergence of geodesics

#### Natasa Macura, Trinity College and Brandeis University

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-complexes
whose universal covers are CAT(0) and have the polynomial divergence
of geodesics of desired degree.