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.
|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|
|Keywords:||Equivariant homotopy theory, Homological algebra, Mackey functor, Slice filtration|
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