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 10 of 10 for “"TQFT"”.
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Topics in quantum topology
… we find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus over given rings of integers. We find bases analogous to the bases defined in [13] for the lattices of the SO(3)-TQFT-theory modules of the torus. Moreover, we discuss the quantization functors (V_{p}, Z_{p}) for p = …
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Bordered Heegaard Floer Homology and four-manifolds with corners
… and to cobordisms between them, yielding a 2+1 TQFT. We discuss an approach to synthesizing these two theories to form a 2+1+1 TQFT, by defining Heegaard Floer invariants for Lefschetz fibrations with corners.
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A 2-categorical extension of the Reshetikhin--Turaev theory
… field theory that extends the Reshetikhin-Turaev TQFT to cobordisms with corners. The source category will be a well chosen 2-category of decorated cobordisms with corners and the target bicategory will be the Kapranov-Voevodsky 2-vector spaces.</p>
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An algebro-geometric study of two models of quantum computaiton
… space-time, what structural properties of a TQFT govern its computational power? When restricted to a space-time with space-like degrees of freedom represented by a smooth surface of genus g, we answer the first question by observing a q⁹-fold degeneracy in the ground state of the TQFT …
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Spectral Fukaya Categories for Liouville Manifolds
… and stably framed. We then develop a basic TQFT formalism, in the stable homotopy category, for producing operations on these Floer homotopy types from families of punctured Riemann surfaces. As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer …
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Bordered Heegaard Floer Homology, Satellites, and Decategorification
… invariants for closed 3-manifolds. We study the TQFT properties of this invariant corresponding to gluing, as well as its connections to sutured Floer homology. As one application, we show that the pairing theorem for bordered Floer homology categorifies the classical Alexander polynomial formula …
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Floer cohomology in the mirror of the projective plane and a binodal cubic curve
… techniques of Lefschetz fibrations and the TQFT counting sections of such fibrations. We also show that our results agree with the tropical analog proposed by Abouzaid-Gross-Siebert. Extensions to a restricted class of singular affine manifolds and to mirrors of the complements of components …
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Classical and quantum gravity with Ashtekar variables
… described by a topological quantum field theory (TQFT) of the Donaldson-Witten type and an Abelian antiinstanton phase wherein self-interactions of the gravitational fields produce symmetry breaking from SO(3) to U(1). The full theory is much richer and includes fluctuations which bring the system …
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The Seiberg-Witten equations on manifolds with boundary
… to provide analytic groundwork for Donaldson's TQFT approach to the Seiberg-Witten invariants of closed 3-manifolds. Finally, in Part Three, we study analytic aspects of the Seiberg-Witten equations on a cylindrical 4-manifold supplied with Lagrangian boundary conditions of the type coming from …
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Gauged Linear Sigma Model and Mirror Symmetry
This thesis is devoted to the study of gauged linear sigma models (GLSMs) and mirror symmetry. The first chapter of this thesis aims to introduce some basics of GLSMs and mirror symmetry. The second chapter contains the author's contributions to new exact results for GLSMs obtained by applying …