The homology of configuration spaces of trees with loops

Chettih, Safia; Lütgehetmann, Daniel

doi:10.2140/agt.2018.18.2443

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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

DOI: 10.2140/agt.2018.18.2443

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.

Keywords

configuration spaces, graphs, Mayer–Vietoris spectral sequence

Mathematical Subject Classification 2010

Primary: 55R80

Secondary: 57M15

References

Publication

Received: 26 July 2017

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/

Volume 18, issue 4 (2018)