Configuration space in a product

John D. Wiltshire-Gordon

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arXiv · 1808.08894

Configuration space in a product

John D. Wiltshire-Gordon

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Abstract

Given a finite graph G and a topological space Z, the graphical configuration space Conf(G, Z) is the space of functions V(G) -> Z so that adjacent vertices map to distinct points. We provide a homotopy decomposition of Conf(G, X x Y) in terms of the graphical configuration spaces in X and Y individually. By way of application, we prove a stabilization result for homology of configuration space in X x C^p as p goes to infinity. We also compute the homology of Conf(K_3,T)/T, the space of ordered triples of distinct points in a torus T of rank r, where configurations are considered up to translation. In Section 2, we give an algorithm for computing homology of configuration space in a product of simplicial complexes. The method is applied to products of some sans-serif capital letters in Example 2.12.

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John D. Wiltshire-Gordon. 2018-08-27. Configuration space in a product. https://arxiv.org/abs/1808.08894

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