Secondary Homological Stability for Unordered Configuration Spaces

Reason: This thesis is pending publication in a journal.

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Secondary Homological Stability for Unordered Configuration Spaces

thesis
posted on 26.04.2022, 19:16 authored by Zachary S HimesZachary S Himes

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.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Jeremy Miller

Additional Committee Member 2

Ralph Kaufmann

Additional Committee Member 3

Sam Nariman

Additional Committee Member 4

Manuel Rivera

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