Hearing the shape of inequivalent spin structures and exotic Dirac operators

Abstract

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 , Z 2 ) that rules a C ̌ ech 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.