Master Thesis Elmendorf’s Theorem for Cofibrantly Generated Model Categories
نویسندگان
چکیده
Elmendorf’s Theorem in equivariant homotopy theory states that for any topological group G, the model category of G-spaces is Quillen equivalent to the category of continuous diagrams of spaces indexed by the opposite of the orbit category of G with the projective model structure. For discrete G, Bert Guillou explored equivariant homotopy theory for any cofibrantly generated model category C and proved an analogue of Elmendorf’s Theorem assuming that C has ”cellular” fixed point functors. We will generalize Guillou’s approach and study equivariant homotopy theory also for topological, cofibrantly generated model categories. Elmendorf’s Theorem will be recovered for G a compact Lie group or a discrete group. Advisor: Prof. Jesper Grodal University of Copenhagen Supervisor: Prof. Karin Baur ETH Zurich
منابع مشابه
The University of Chicago Algebraic Model Structures a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy
In Part I of this thesis, we introduce algebraic model structures, a new context for homotopy theory in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads and prove “algebraic” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that every cofibrantly generated model structure in the usual sense un...
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