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Secondary Homological Stability for Unordered Configuration Spaces

<p>Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological stability for the homology of the unordered configuration spaces of a connected manifold. The main difficulty is the case that the manifold is compact because there are no obvious maps inducing stability and the homology eventually is periodic instead of stable. We resolve this issue by constructing a new chain-level stabilization map for configuration spaces.</p>

  1. 10.25394/pgs.19660593.v1
Identiferoai:union.ndltd.org:purdue.edu/oai:figshare.com:article/19660593
Date26 April 2022
CreatorsZachary S Himes (12448314)
Source SetsPurdue University
Detected LanguageEnglish
TypeText, Thesis
RightsCC BY 4.0
Relationhttps://figshare.com/articles/thesis/Secondary_Homological_Stability_for_Unordered_Configuration_Spaces/19660593

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