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.
Results
Showing 1 to 20 of 24 for “"Groupoids"”.
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Abelianization of groupoids and Lie algebroids
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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A model for groupoids of homeomorphisms
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1982
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Homology, cohomology and extensions of ordered groupoids
… homology, cohomology and extensions of ordered groupoids. We study the simplicial homology of ordered groupoids. We also discuss the (co)homology of the set of identities of ordered groupoids and relate the cohomology of the set of identities of an ordered groupoid to the cohomology of the …
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Local symplectic groupoids and the SGA equation
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Symplectic foliations, currents, and local Lie groupoids
… calibrated symplectic foliations, and local Lie groupoids. Calibrated symplectic foliations are one possible generalization of taut foliations of 3-manifolds to higher dimensions. Their study has been popular in recent years, and we collect several interesting results. We then show how de Rham’s …
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Derived Lie Infinity-Groupoids And Algebroids In Higher Differential Geometry
… in higher geometry using derived Lie $\infty$-groupoids and algebroids. We construct homotopical algebras for derived Lie $\infty$-groupoids and algebroids and study their homotopy-coherent representations. Then we apply these tools in studying singular foliations and their characteristic …
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Analytic and holomorphic structures in Lie groupoids, algebroids, and Poisson geometry
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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Stacks in Poisson geometry
… the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The second chapter discusses standard concepts in …
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The functorial semantics of Lie theory
Ehresmann’s introduction of differentiable groupoids in the 1950s may be seen as a starting point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids and Lie groupoids) and sketch theory. This thesis uses tangent categories to build a bridge between these two …
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Homotopy Theory of Monoids and Group Completion
… group completion of monoids in the category of ω-groupoids for the Gray tensor product is isomorphic to group completion for simplicial monoids in low degrees. Finally we exploit the connection of ω-groupoids with the theory of rewriting for presentations of monoids to calculate the second …
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On mobs with certain group-like properties
Topological groupoids with"approximate" inverses are studied. In the compact case, these"approximate" inverses turn out to be true inverses. Examples of groupoids wL:h"approximate" inverses are given in the section dealing with function spaces. Using the classical construction of Haar as a guide, …
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Quasi-metric geometry
… we look at functions on abstract objects called groupoids, which is yet another step toward generality, since the objects we consider here contain the class of quasi-metrics. Dealing with groupoids is useful because it provides a natural structure into which quasi-metrics and quasi-norms fit. …
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Continuous and discrete aspects of Lagrangian field theories with nonholonomic constraints
… discrete field theories taking values in Lie groupoids. It is shown that many previously known discrete field theories are particular instances of Lie groupoid field theories, and the geometry of Lie groupoids is used to construct a unifying framework for this class. In two further chapters, …
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A homotopy theory for stacks
… 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 objects. This allows us to compare the different definitions of stacks and show that …
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Partial dynamical systems and AF C*-algebras
… utilizing the connections between C*-algebras, groupoids, and inverse semigroups, we obtain a characterization theorem, in terms of dynamical systems, of approximately finite-dimensional (AF) C*-algebras. The dynamical systems considered in this characterization consist of partially defined …
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Connections between binary systems and admissible topologies
… groups. Various classes of topologically trivial groupoids are examine, and it is shown that there exist topologically trivial groupoids of every order. G is said to be right (analogously left) topologically trivial if one can find elements a·b = c in G and U<sub>c</sub> in T such that …
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Lie Theory in Generalized Kähler Geometry
… Morita equivalences of symplectic double groupoids, 2-morphisms between Morita equivalences, and multiplicative LS bisections in order to access the underlying holomorphic data, and smooth data associated with GK structures. We then employ techniques from Poisson Geometry, such as gauge …
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Steinberg algebra and Leavitt path algebras
… susceptible to a new approach using topological groupoids. Taking a special kind of groupoid G, one can construct an R-algebra called the Steinberg algebra of G. Many interesting classes of algebras, including Leavitt path algebras, can be obtained from this process. This dissertation is an …
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Kaleidoscopic decomposition, classification of finite branched coverings of the sphere and path-lifting algorithms
… original approach based on finite combinatorial groupoids, which allows us to prove novel results addressing some of their topological properties (like the monodromy or the group of automorphisms), to completely characterize their regularity in simple algebraic terms, and to study and relate …
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A groupoid approach to geometric mechanics
… or incompressible, irrotational or not. By using groupoids we generalize Arnold’s diffeomorphism group framework for fluid flows to show that the well-known equations governing the motion of these various systems can be viewed as geodesic equations (or more generally, Newton’s equations) written …
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