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Geodesics in CAT(0) cubical complexes |
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| Authors: | Federico Ardila Seth Sullivant |
| Institution: | a Department of Mathematics, San Francisco State University, San Francisco, CA 94132, United States b Department of Mathematics, University of California Berkeley, Berkeley, CA 94720, United States c Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States |
| Abstract: | 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. |
| Keywords: | primary 05E99 secondary 51F99 68R05 68U05 |
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