Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7manifolds
Abstract
We extend the adiabatic limit formula for etainvariants by BismutCheeger 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 EellsKuiper and tinvariants 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 DOI:
 10.48550/arXiv.1108.5614
 arXiv:
 arXiv:1108.5614
 Bibcode:
 2011arXiv1108.5614G
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology;
 58J28 (primary);
 57R55 (secondary)
 EPrint:
 54 pages, LaTeX