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MBC_THESIS.pdf (3.54 MB)
ETD Abstract Container
Abstract Header
Retractive operadic algebras in spectra and completions
Author Info
Carr, Matthew B
ORCID® Identifier
http://orcid.org/0009-0006-6358-7584
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1681959857595088
Abstract Details
Year and Degree
2023, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
Working in the context of operadic algebras in modules over the sphere spectrum, we study completions with respect to invariants centered away from the base point—that is, centered at a fixed operadic algebra $Y$. We show that for retractive objects admitting $0$-connected structural maps $Y\to X$, the Bousfield-Kan completion map $X\to X^{\sma}_{\Omega_Y^k\Sigma_Y^k}$ is an equivalence for $1\le k\le\infty$. This generalizes completion results of Blomquist and Ching-Harper when $Y=\ast$. The manner of our attack will require us to pick up and develop Hovey's stabilization machinery and carefully study the homotopy theory and stabilization of categories of retractive objects.
Committee
John Harper (Advisor)
Vidhyanath Rao (Committee Member)
Niles Johnson (Committee Member)
Subject Headings
Mathematics
Keywords
Homotopy theory, algebraic topology
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Citations
Carr, M. B. (2023).
Retractive operadic algebras in spectra and completions
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1681959857595088
APA Style (7th edition)
Carr, Matthew.
Retractive operadic algebras in spectra and completions.
2023. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1681959857595088.
MLA Style (8th edition)
Carr, Matthew. "Retractive operadic algebras in spectra and completions." Doctoral dissertation, Ohio State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=osu1681959857595088
Chicago Manual of Style (17th edition)
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Document number:
osu1681959857595088
Download Count:
56
Copyright Info
© , some rights reserved.
Retractive operadic algebras in spectra and completions by Matthew B Carr is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.