Purdue University Graduate School
Browse

Secondary Homological Stability for Unordered Configuration Spaces

Reason: This thesis is pending publication in a journal.

1

year(s)

10

month(s)

13

day(s)

until file(s) become available

Secondary Homological Stability for Unordered Configuration Spaces

thesis
posted on 2022-04-26, 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

Usage metrics

    Categories

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC