Monday, 1 August, 14:45-15:45, Room 4102


Piotr Przytycki (Polish Academy of Sciences


Square Complexes and Simplicial Non-positive Curvature


Joint work with Tomasz Elsner. We prove that each nonpositively curved
square VH-complex can be turned functorially into a locally 6-large
simplicial complex of the same homotopy type. It follows that any group
acting geometrically on a CAT(0) square VH-complex is systolic. In
particular the product of two finitely generated free groups is systolic,
which answers a question of Daniel Wise. On the other hand, we exhibit an
example of a compact non-VH nonpositively curved square complex, whose
fundamental group is neither systolic, nor even virtually systolic.

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