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Constructing non-positively curved spaces and groups. (English) Zbl 1237.20035
Bridson, Martin R. (ed.) et al., Geometric and cohomological methods in group theory. Papers from the London Mathematical Society symposium on geometry and cohomology in group theory, Durham, UK, July 2003. Cambridge: Cambridge University Press (ISBN 978-0-521-75724-9/pbk). London Mathematical Society Lecture Note Series 358, 162-224 (2009).
Summary: The theory of non-positively curved spaces and groups is tremendously powerful and has enormous consequences for the groups and spaces involved. Nevertheless, our ability to construct examples to which the theory can be applied has been severely limited by an inability to test – in real time – whether a random finite piecewise Euclidean complex is non-positively curved. In this article I focus on the question of how to construct examples of non-positively curved spaces and groups, highlighting in particular the boundary between what is currently do-able and what is not yet feasible. Since this is intended primarily as a survey, the key ideas are merely sketched with references pointing the interested reader to the original articles.
For the entire collection see [Zbl 1197.20001].

20F65 Geometric group theory
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
57M07 Topological methods in group theory
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