Geodesics in CAT(0) Cubical Complexes

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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Federico Ardila, Megan Owen, Seth Sullivant
• Keywords: CORR 2011, Cubical Complex, Cubical Complexes, Education, Global Non-positive Curvature