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Showing 1 to 11 of 11 for “"index theorem"”.
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THE INDEX THEOREM FOR QUASI-TORI
The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected …
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Foliations and exotic index theory
… map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation exotic index theorem can be …
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Index theorems and magnetic monopoles on asymptotically conic manifolds
In this thesis, I investigate the index of Callias type operators on asymptotically conic manifolds (also known as asymptotically locally Euclidean manifolds or scattering manifolds) and give an application to the moduli space of magnetic monopoles on these spaces. The index theorem originally due …
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Fermions in Yang-Mills gauge theories: invariance, covariance and topology
… give the so-called anomalies. The Atiyah-Singer index theorem is seen to be a very powerful tool to calculate the topological invariants that characterize the anomalies. The index theorem also gives topological invariants describing the failure of covariance of the fermion propagator.
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On a pseudodifferential calculus with modest boundary decay condition
… a detailed proof of the Atiyah-Patodi-Singer index theorem, including a review of Dirac operators of product type and construction of the heat kernel, is presented.</p>
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Aspects of index theory
Index theory is the theory of linear maps with finite dimensional nullspaces and cokernels. In particular, the index of such a map is the dimension of its nullspace minus that of its cokernel. We survey some aspects of this theory in this thesis. In particular, the first chapter talks about general …
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Dirac operators and monopoles with singularities
… In the first part of the thesis, we prove an index theorem for Dirac operators of conic singularities with codimension 2. One immediate corollary is the generalized Rohklin congruence formula. The eta function for a twisted spin Dirac operator on a circle bundle over a even dimensional spin …
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Genera via Deformation Theory and Supersymmetric Mechanics
… prove a super-version of Nest-Tsygan’s algebraic index theorem, generalizing work of Engeli. This work is inspired by the appearance of the same genera in three related stories: index theory, trace methods in deformation theory, and partition functions in quantum field theory. Using the trace …
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On Semi-isogenous Mixed Surfaces
… only curves. The second approach exploits Hodge index theorem to bound the number of exceptional curves that live on a Semi-isogenous Mixed Surface.
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A proof of Tsygan's formality conjecture for an arbitrary smooth manifold
… new generalizations of the Atiyah-Patodi-Singer index theorem and the Riemann-Roch-Hirzebruch theorem. Despite this pivotal role in the traditional investigations and the efforts of various people the most general version of Tsygan's formality conjecture has not yet been proven. In my thesis I …
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An Orbifold Geometry in Holography, or: How the spindle fits into supergravity and supersymmetric quantum field theory
L'abstract è presente nell'allegato / the abstract is in the attachment