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.
|Advisor:||May, J. Peter|
|Commitee:||Elmendorf, Anthony, May, J. Peter|
|School:||The University of Chicago|
|School Location:||United States -- Illinois|
|Source:||DAI-B 75/11(E), Dissertation Abstracts International|
|Keywords:||G-mackey functors, H-mackey functors, Stable homotopy theory|
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