Dissertation/Thesis Abstract

Mackey Functors, Equivariant Eilenberg-Mac Lane Spectra and Their Slices
by Zeng, Mingcong, Ph.D., University of Rochester, 2018, 135; 10842039
Abstract (Summary)

This thesis has three parts. In the first part, we analyze the homological algebra of cohomological Mackey functors, for cyclic p-groups. We study basic properties of homological algebra of cohomological Mackey functors, give examples of computations and study how homological invariants interact with subgroups and quotient groups. The second part consists of computation of RO(G)-graded ho- motopy Mackey functors of HZ, the Eilenberg-Mac Lane spectrum of the constant Mackey functor of integers, and how these computations further help in under- standing the homological algebra. The third part is an investigation into the slice filtration of [HHR16] and [Ull13a]. We prove a theorem on equivalence of slice categories for cyclic p-groups, then gives constructions of slices of suspensions of HZ, especially for cyclic groups of order p2.

Indexing (document details)
Advisor: Ravenel, Douglas C.
Commitee: Cohen, Frederick R., Garzione, Carmala, Rajeev, Sarada
School: University of Rochester
Department: Arts and Sciences
School Location: United States -- New York
Source: DAI-B 80/02(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Equivariant homotopy theory, Homological algebra, Mackey functor, Slice filtration
Publication Number: 10842039
ISBN: 978-0-438-38098-1
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