Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 59 for “"Homotopy theory"”.
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Operads and Homotopy Theory
… notion of a group operad is proposed and then a theory of group operads is developed, extending the classical theories of groups, spaces with actions of groups, covering spaces and classifying spaces of groups. Group operads apply to homotopy theory via their associated monads. As an application, …
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Twisted stable homotopy theory
… two natural interpretations of a twist of stable homotopy theory. The first interpretation of a twist is as a nontrivial bundle whose fibre is the stable homotopy category. This kind of radical global twist forms the basis for twisted parametrized stable homotopy theory, which is introduced and …
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Homotopy theory and topoi
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.
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Unstable chromatic homotopy theory
In this thesis, I study unstable homotopy theory with chromatic methods. Using the v, self maps provided by the Hopkins-Smith periodicity theorem, we can decompose the unstable homotopy groups of a space into its periodic parts, except some lower stems. For fixed n, using the Bousfield-Kuhn functor …
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Homotopy theory of moduli spaces
… their moduli spaces, that is their study up to homotopy or gauge equivalence. Within the three papers cited above (and thus within this thesis), three different applications of Maurer-Cartan elements are demonstrated. The first application constructs certain moduli spaces as models for unbased …
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A homotopy theory for stacks
We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal homotopy theory, in which stacks play the special role of the fibrant …
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Gröbner bases in rational homotopy theory
… Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. The main obstacle is the lack of an Eckmann-Hilton dual to the Kiinneth theorem with which to understand the homotopy of a …
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Norms and transfers in motivic homotopy theory
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-08-01
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Homotopy Theory of Monoids and Group Completion
… several complete and partial models for the homotopy theory of monoids and the derived functor of group completion. We show that there is a simplicial model structure on the category of reduced simplicial sets that is Quillen equivalent to the Quillen model structure of simplicial monoids. …
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On the Homotopy Theory of Stratified Spaces
… Treumann, and Lurie. To prove this stratified homotopy hypothesis, we define combinatorial simplicial model structure on the category of simplicial sets over the nerve of 𝑃 whose underlying ∞-category is the ∞-category Strₚ. This model structure on P-stratified simplicial sets allows us to …
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Chromatic homotopy theory in HF_p based synthetic spectra
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms
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On Hochschild type constructions in motivic homotopy theory
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2027-08-01
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Investigations into the categorical foundations of homotopy theory
… an account of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives …
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Studying the Space of Almost Complex Structures on a Manifold Using de Rham Homotopy Theory
… result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the …
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Weakly enriched higher categories
… thesis is to begin to lay the foundations for a theory of enriched [infinity]categories. We introduce a definition of such objects, based on a non-symmetric version of Lurie's theory of [infinity]-operads. Our first main result is a construction of the correct homotopy theory of enriched …
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Derived mapping spaces as models for localizations by Jennifer E. French.
… on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into two parts. The first part is a reflection on M. Mandell's model for p-adic homotopy theory. …
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A motivic norm structure on equivariant algebraic K-theory
Equivariant motivic homotopy theory is a homotopy theory of schemes with algebraic group actions. This thesis is mainly divided into two parts. In the first part, we define four model categories of motivic spectra that present the $\infty$-category $\SH^G(S)$. We use the model categorical setup to …
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Stability and distributivity over orbital [infinity]-categories/
Let G be a finite group. The homotopy theory of topological spaces with an action of G has provided important applications in many parts of homotopy theory and geometry. An especially important role has been played by the so-called "norm maps". In this thesis we develop a characterization of the …
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