#### Volume 18, issue 4 (2018)

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The homology of configuration spaces of trees with loops

### Safia Chettih and Daniel Lütgehetmann

Algebraic & Geometric Topology 18 (2018) 2443–2469
##### 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.

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##### Keywords
configuration spaces, graphs, Mayer–Vietoris spectral sequence
Primary: 55R80
Secondary: 57M15
##### Publication
Revised: 26 November 2017
Accepted: 24 January 2018
Published: 26 April 2018
##### Authors
 Safia Chettih Department of Mathematics Reed College Portland, OR United States http://people.reed.edu/~safia/ Daniel Lütgehetmann Department of Mathematics The School of Natural and Computing Sciences University of Aberdeen Aberdeen United Kingdom https://homepages.abdn.ac.uk/daniel.lutgehetmann/pages/