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Spin structures and spectra of ℤ2 k-manifolds

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Abstract.

We give necessary and sufficient conditions for the existence of pin± and spin structures on Riemannian manifolds with holonomy group ℤ2 k. For any n≥4 (resp. n≥6) 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 ± (resp. spin) structure whereas M 2 does not.

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Authors and Affiliations

  1. FaMAF–CIEM, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina

    Roberto J. Miatello & Ricardo A. Podestá

Authors
  1. Roberto J. Miatello
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  2. Ricardo A. Podestá
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Correspondence to Ricardo A. Podestá.

Additional information

Mathematics Subject Classification (2000):58J53, 57R15, 20H15

Partially supported by Conicet and grants from SecytUNC, Foncyt and AgCba.

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Miatello, R., Podestá, R. Spin structures and spectra of ℤ2 k-manifolds. Math. Z. 247, 319–335 (2004). https://doi.org/10.1007/s00209-003-0615-y

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  • DOI: https://doi.org/10.1007/s00209-003-0615-y

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