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An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra

Clark, Duncan
http://rave.ohiolink.edu/etdc/view?acc_num=osu161702647643754

Abstract Details

2021, Doctor of Philosophy, Ohio State University, Mathematics.
The aim of this dissertation is three-fold: (i) we construct a natural highly homotopy coherent operad structure on the derivatives of the identity functor on structured ring spectra which can be described as algebras over an operad O in spectra, (ii) we prove that every connected O-algebra has a naturally occurring left action of the derivatives of the identity, and (iii) we show that there is a naturally occurring weak equivalence of highly homotopy coherent operads between the derivatives of the identity on O-algebras and the operad O. Along the way, we introduce the notion of N-colored operads with levels which, by construction, provides a precise algebraic framework for working with and comparing highly homotopy coherent operads, operads, and their algebras. We also show that similar techniques may be used to provide a new description of an operad structure for the Goodwillie derivatives of the identity in spaces and describe an explicit comparison map from spaces to algebras over such operad.
John Harper (Advisor)
Niles Johnson (Committee Member)
Crichton Ogle (Committee Member)
128 p.
Mathematics
Algebraic topology, homotopy theory, functor calculus, structured ring spectra

Recommended Citations

Citations

  • Clark, D. (2021). An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu161702647643754

    APA Style (7th edition)

  • Clark, Duncan. An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra. 2021. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu161702647643754.

    MLA Style (8th edition)

  • Clark, Duncan. "An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu161702647643754

    Chicago Manual of Style (17th edition)

osu161702647643754
319
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