The Homology of Configuration Spaces of Trees with Loops

Abstract

We show that the homology of ordered configuration spaces of finite trees with loops is torsion free. We introduce configuration spaces with sinks, which allow for taking quotients of the base space. Furthermore, we give a concrete generating set for all homology groups of configuration spaces of trees with loops and the first homology group of configuration spaces of general finite graphs. An important technique in the paper is the identification of the $E^1$-page and differentials of Mayer-Vietoris spectral sequences for configuration spaces.

arXiv comment21 pages, 7 figures. Revised Proposition 2.3, other minor changes

References in corpus (3)

• Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
• Discrete Morse theory and graph braid groups
• Topology of configuration space of two particles on a graph, II

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