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 13 of 13 for “"Operads"”.
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Operads and Homotopy Theory
… 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, all braid …
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Operads and moduli spaces
… of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics. We consider the …
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Operads, modules and higher Hochschild cohomology
In this thesis, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad [epsilon]d of little d-dimensional disks, we show that each (d - 1) manifold gives rise to a theory of modules over …
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Deformation complexes of algebraic operads and their applications
Given a reduced cooperad C, we consider the 2-colored operad Cyl(C) which governs diagrams U: V -> W, where V, W are Cobar(C)-algebras, and U is an infinity-morphism. We then investigate the deformation complexes of Cyl(C) and Cobar(C). Our main result is that the restriction maps between between …
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Spaces of algebra structures and cohomology of operads
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
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Bar constructions for topological operads and the Goodwillie derivatives of the identity
… we extend the bar construction to modules over operads (and, dually, to comodules over cooperads) and show that based spaces naturally give rise to modules over the operad formed by the derivatives of the identity.
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On THH and TAQ of Commutative S-Algebras
… enriched over the homology of little n-cubes operads and discuss the relationship between functors defined via functional equations and operads. In addition, we compute the differentials of the forgetful functor from the category of n-Poisson algebras in terms of the homology of configuration …
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Weakly enriched higher categories
… version of Lurie's theory of [infinity]-operads. Our first main result is a construction of the correct homotopy theory of enriched [infinity]-categories as a localization of an "algebraic" homotopy theory defined using [infinity]-operads; this is joint work with David Gepner. We then …
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Connecting models of configuration spaces: From double loops to strings
… examine the connection between two <em>E</em> 2 operads, namely the little 2-cubes operad <em>C</em> 2 itself and the operad of spineless cacti. To this end, we construct a new suboperad of <em>C</em>2, which we name the operad of tethered 2-cubes. Much of our analysis involves examining trees …
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RECURSIVELY GENERATING FORMALITY QUASI-ISOMORPHISMS WITH APPLICATIONS TO DEFORMATION QUANTIZATION
… can be "demystified" for a large class of dg-operads, by showing that they can be constructed recursively via an algorithm that builds them from systems of linear equations over Q, given certain assumptions on H(O).
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The Koszul dual to n-Lie, n-Com algebras, and Young tableaux
… the Specht module $S^{(n,n-1)}$. We combine the operads $n$-Lie and $m$-Com to construct the operad $(m,n)-Poiss$, where the rewriting rule that relates them is through a generalized Leibniz rule. We generalize the above Koszul duality to different types of generalization of $Lie$ and $Com$ which …
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Mapping spaces of algebras over iterated +-construction for polynomial monads
… over the associative operad for non-symmetric operads. The 0-dimensional bimodules are a sequence of categories of opetopes, with each the full subcategory of the next, which generalizes the simplicial category ∆ and the dentroidal category of planar trees Ωp. We show that an explicit double …
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An inductive approach to ω-categories and their computads
… that avoids the technology of globular operads. This new description permits direct proofs of important results via structural induction, and we use this to give new proofs that every ω-category is equivalent to a free one, and that the category of computads with generator-preserving …