
handle: 10347/26156
[EN] This work is a mostly self-contained survey on Dirac operators. It starts by laying the fundamental building blocks at the heart of spin geometry, specifically its elemental geometrical and algebraic aspects. Thus, the concepts of vector and principal bundles over manifolds, Clifford algebras, the Pin and Spin groups, the spin representation and the spinor bundle are explored. A brief commentary on connections and linear differential operators on manifolds is also provided. Subsequently, the fundamental Dirac operator is presented, along with a review of its most important basic properties. The last section is devoted to a study of the Dirac spectrum on compact manifolds, including some explicit computations and bounds of the lower nonzero eigenvalue.
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