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An, Byung Hee
기하학 수리물리 연구단
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Edge stabilization in the homology of graph braid groups

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Title
Edge stabilization in the homology of graph braid groups
Author(s)
Byung Hee An; Gabriel C. Drummond-Cole; Ben Knudsen
Subject
CONFIGURATION-SPACES, ; QUANTUM STATISTICS, ; STABILITY
Publication Date
2020-03
Journal
GEOMETRY & TOPOLOGY, v.24, no.1, pp.421 - 469
Publisher
GEOMETRY & TOPOLOGY PUBLICATIONS
Abstract
© The Author(s) 2020. We introduce a novel type of stabilization map on the configuration spaces of a graph which increases the number of particles occupying an edge. There is an induced action on homology by the polynomial ring generated by the set of edges, and we show that this homology module is finitely generated. An analogue of classical homological and representation stability for manifolds, this result implies eventual polynomial growth of Betti numbers. We calculate the exact degree of this polynomial, in particular verifying an upper bound conjectured by Ramos. Because the action arises from a family of continuous maps, it lifts to an action at the level of singular chains which contains strictly more information than the homology-level action. We show that the resulting differential graded module is almost never formal over the ring of edges
URI
https://pr.ibs.re.kr/handle/8788114/8714
DOI
10.2140/gt.2020.24.421
ISSN
1465-3060
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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