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Deletion and
contraction in configuration spaces of graphs
Sanjana Agarwal, Maya Banks, Nir Gadish and Dane Miyata |
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Algebraic & Geometric Topology 21 (2021) 3663–3674
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Abstract |
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Our aim is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and identify the homotopy cofibers in terms of configuration spaces of simpler graphs. The construction’s main benefit lies in making the operations functorial — in particular, graph minors give rise to compatible maps at the level of fundamental groups as well as generalized (co)homology theories. As applications we provide a long exact sequence for half-edge deletion in any generalized cohomology theory, compatible with cohomology operations such as the Steenrod and Adams operations, allowing for inductive calculations in this general context. We also show that the generalized homology of unordered configuration spaces is finitely generated as a representation of the opposite graph-minor category. |
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Keywords
configuration spaces, graphs, graph minor, edge
contraction, edge deletion, homology, cohomology, homotopy
cofiber, mapping cone, braid groups
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Mathematical Subject Classification
Primary: 55R80
Secondary: 05C10, 20F36
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References |
Publication
Received: 20 July 2020
Revised: 1 November 2020
Accepted: 11 December 2020
Published: 28 December 2021
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Authors |
| Sanjana Agarwal | |
| Department of Mathematics Indiana University Bloomington, IN United States |
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| Maya Banks | |
| Department of Mathematics University of Wisconsin Madison, WI United States |
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| Nir Gadish | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Dane Miyata | |
| Department of Mathematics University of Oregon Eugene, OR United States |
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