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

Hearing the shape of inequivalent spin structures and exotic Dirac operators