Dissertation/Thesis Abstract

Two topics in stable homotopy theory
by Hoyer, Rolf, Ph.D., The University of Chicago, 2014, 93; 3627837
Abstract (Summary)

We give a definition of a norm functor from H-Mackey functors to G-Mackey functors for G a finite group and H a subgroup of G. We check that this agrees with the construction of Mazur in the case G cyclic of prime power order and also with the topological definition of norm, which has an algebraic presentation due to Ullman. We then use this norm functor to give a characterization of Tambara functors as monoids of an appropriate flavor.

The second chapter is part of a joint project with Andrew Baker. We consider what happens when we take the sphere spectrum, and kill elements of homotopy in an E fashion. This process starts with the element 2 and is repeated in order to kill all higher homotopy groups. We provide methods for identifying spherical classes and for understanding the Dyer-Lashof action at each step of the construction. We outline how this construction might be used to compute the André-Quillen homology of Eilenberg-MacLane spectra considered as algebras over the sphere spectrum.

Indexing (document details)
Advisor: May, J. Peter
Commitee: Elmendorf, Anthony, May, J. Peter
School: The University of Chicago
Department: Mathematics
School Location: United States -- Illinois
Source: DAI-B 75/11(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: G-mackey functors, H-mackey functors, Stable homotopy theory
Publication Number: 3627837
ISBN: 9781321033380