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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 E1–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/