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Lecture Notes on Spin Geometry
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Lecture Notes on Spin Geometry
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We review the Atiyah-Singer Index theorem and some applications. Only basic knowledge of differential geometry and Lie groups is required.
Forward citations
Cited by 3 Pith papers
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The reduced Dirac structure of General Relativity on manifolds with corners
The reduced corner phase space of Palatini–Cartan gravity is a Dirac structure—the graph of a Poisson bivector—yielding a strict BF2V theory.
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A spinor-adapted geometric approach for nonlinear Dirac systems and its application to a tensorial wave-Dirac system near Minkowski spacetime
Small-data solutions of a nonlinear tensorial wave-Dirac system on non-trapping asymptotically flat spacetimes are shown to exist globally with quantitative weighted-energy decay.
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The reduced Dirac structure of General Relativity on manifolds with corners
Four-dimensional Palatini–Cartan gravity on manifolds with corners reduces to a maximal Dirac structure that is the graph of a Poisson bivector, equivalently an affine BF-like BF²V corner theory.
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