Hearing the shape of inequivalent spin structures and exotic Dirac operators
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 H1(M,Z2) 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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