Spin structures and spectra of $Z_2^k$-manifolds

Details Spin structures and spectra of $Z_2^k$-manifolds Spin structures and spectra of $Z_2^k$-manifolds

2003-11-20

arxiv.org/abs/math/0311354v1

Mathematics

Differential Geometry

15 pages. Accepted for publication in Math. Z

Scientific paper

We give necessary and sufficient conditions for the existence of pin+, pin- and spin structures on Riemannian manifolds with holonomy group $Z_2^k$. For any n>3 (resp. n>5) we give examples of pairs of compact manifolds (resp. compact orientable manifolds) M_1, M_2, non homeomorphic to each other, that are Laplace isospectral on functions and on p-forms for any p and such that M_1 admits a pin+, or pin-, (resp. spin) structure whereas M_2 does not.

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