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Subdivisional spaces and graph braid groups

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Title
Subdivisional spaces and graph braid groups
Author(s)
Byung Hee An; Gabriel C. Drummond-Cole; Ben Knudsen
Publication Date
2019
Journal
DOCUMENTA MATHEMATICA, v.24, no.0, pp.1513 - 1583
Publisher
UNIV BIELEFELD
Abstract
We study the problem of computing the homology of the configuration spaces of a finite cell complex X. We proceed by viewing X, together with its subdivisions, as a subdivisional space—a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we decompose X and show that the homology of the configuration spaces of X is computed by the derived tensor product of the Morse complexes of the pieces of the decomposition, an analogue of the monoidal excision property of factorization homology. Applying this theory to the configuration spaces of a graph, we recover a cellular chain model due to Świątkowski. Our method of deriving this model enhances it with various convenient functorialities, exact sequences, and module structures, which we exploit in numerous computations, old and new. C.2018 FLZ Karlsruhe GmbH
URI
https://pr.ibs.re.kr/handle/8788114/6964
ISSN
1431-0643
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Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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