Titlebook: CAT(0) Cube Complexes; An Introduction Petra Schwer Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to S

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Introduction,ong such spaces, . cube complexes play a significant and successful role. Their metric and combinatorial structure give rise to several nice algebraic properties for groups acting geometrically, that is, properly and cocompactly, on them. The existence of such a cocompact cubulation of a group . imp

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Minatory

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Hyperplanes and Half-Spaces,inside 2-cubes and carry themselves the structure of a . cube complexes of a smaller dimension. Each hyperplane in a . cube complex divides the complex into two disjoint half-spaces. Surprisingly the combinatorics of the relative position of the hyperplanes and half-spaces completely determines the

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A Panoramic Tour,f actions on . cube complexes in analogy to similar results about actions on trees. To learn more about one of the many algebraic consequence for groups acting nicely on . cube complexes, we prove, in Sect. 7.2, that all such groups satisfy the Tits alternative. Admitting an action on a special cube

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abduction

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