Geodesics in CAT(0) Cubical Complexes

Details Geodesics in CAT(0) Cubical Complexes Geodesics in CAT(0) Cubical Complexes

2011-01-12

arxiv.org/abs/1101.2428v1

Mathematics

Combinatorics

27 pages, 7 figures

Scientific paper

We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed any interval in the integer lattice cubing of its dimension.

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