JournalsjemsVol. 16, No. 12pp. 2499–2555

Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds

  • Sebastian Goette

    Universität Freiburg, Germany
Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds cover
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Abstract

We extend the adiabatic limit formula for η\eta-invariants by Bismut–Cheeger and Dai to Seifert fibrations. Our formula contains a new contribution from the singular fibres that takes the form of a generalised Dedekind sum.

As an application, we compute the Eells–Kuiper and t-invariants of certain cohomogeneity one manifolds that were studied by Dearricott, Grove, Verdiani, Wilking, and Ziller. In particular, we determine the diffeomorphism type of a new manifold of positive sectional curvature.

Cite this article

Sebastian Goette, Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds. J. Eur. Math. Soc. 16 (2014), no. 12, pp. 2499–2555

DOI 10.4171/JEMS/492