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April 2022 Connectivity at infinity for state spaces of complete bipartite graphs
Kristen Mazur, Jon McCammond, John Meier, Ranjan Rohatgi
Rocky Mountain J. Math. 52(2): 667-686 (April 2022). DOI: 10.1216/rmj.2022.52.667

Abstract

The state or configuration space for r vertices on a complete bipartite graph Km,n is a CAT(0) cube complex, which is sometimes interpreted as a parameter space for r robots moving on a Km,n. We combine an analysis of the topology of links of vertices in this complex, the description of a hidden symmetry among the parameters, and known results from the literature to explicitly compute the exact degree to which the universal covers of these complexes are connected at infinity.

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Kristen Mazur. Jon McCammond. John Meier. Ranjan Rohatgi. "Connectivity at infinity for state spaces of complete bipartite graphs." Rocky Mountain J. Math. 52 (2) 667 - 686, April 2022. https://doi.org/10.1216/rmj.2022.52.667

Information

Received: 20 January 2020; Revised: 21 July 2021; Accepted: 21 July 2021; Published: April 2022
First available in Project Euclid: 17 May 2022

Digital Object Identifier: 10.1216/rmj.2022.52.667

Subjects:
Primary: 20F65 , 57M07

Keywords: graph braid groups , topology at infinity

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 2 • April 2022
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