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ETD Abstract Container

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Iterated desuspension and delooping of structured ring spectra

Blomquist, Jacobson Robert
http://rave.ohiolink.edu/etdc/view?acc_num=osu1523477215151452

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Mathematics.
We study completion with respect to the iterated suspension functor on 𝒪-algebras, where 𝒪 is a reduced operad in symmetric spectra. It turns out it is the unit of a derived adjunction comparing 𝒪-algebras with coalgebras over the associated iterated suspension-loop homotopical comonad via the iterated suspension functor. We prove that this derived adjunction becomes a derived equivalence when restricted to 0-connected 𝒪-algebras and r connected Σr Ωr -coalgebras. We also consider the dual picture, using iterated loops to build a cocompletion map from algebras over the iterated loop-suspension homotopical monad to 𝒪-algebras. This is the counit of a derived adjunction, which we prove is a derived equivalence when restricting to r-connected 𝒪-algebras and 0-connected Ωr Σr-algebras. The final chapter also goes through similar analysis in the context of spaces, for iterated suspension, stabilization, and integral chains, as well as the dual picture for iterated loops.
John E Harper (Advisor)
Niles Johnson (Committee Member)
Vidhyanath Rao (Committee Member)
40 p.
Mathematics
homotopy; topology; algebraic topology; completion; simplicial set; operad; algebra over operad; structured ring spectra; suspension; freudenthal suspension; mathematics;

Recommended Citations

Citations

  • Blomquist, J. R. (2018). Iterated desuspension and delooping of structured ring spectra [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1523477215151452

    APA Style (7th edition)

  • Blomquist, Jacobson. Iterated desuspension and delooping of structured ring spectra. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1523477215151452.

    MLA Style (8th edition)

  • Blomquist, Jacobson. "Iterated desuspension and delooping of structured ring spectra." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1523477215151452

    Chicago Manual of Style (17th edition)

osu1523477215151452
316
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This open access ETD is published by The Ohio State University and OhioLINK.