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arXiv · 2003.03619

Hearing the shape of inequivalent spin structures and exotic Dirac operators

R. da Rocha·A. A. Tomaz
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Abstract

Exotic spinor fields arise from inequivalent spin structures on non-trivial topological manifolds, $M$. This induces an additional term in the Dirac operator, defined by the cohomology group $H^1(M,\mathbb{Z}_2)$ that rules a Cech cohomology class. This formalism is extended for manifolds of any finite dimension, endowed with a metric of arbitrary signature. The exotic corrections to heat kernel coefficients, relating spectral properties of exotic Dirac operators to the geometric invariants of $M$, are derived and scrutinized.

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R. da Rocha, A. A. Tomaz. 2020-03-07. Hearing the shape of inequivalent spin structures and exotic Dirac operators. https://doi.org/10.1088/1751-8121%2Fabacdc

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