15 jul 2019 -- 14:30
Aula Tricerri, DiMaI, Firenze
Abstract.
We give examples of Eschenburg biquotients which have disconnected moduli spaces of metrics with positive sectional curvature. The only previously known spaces with this property are homogeneous Aloff-Wallach spaces. We use the Kreck-Stolz invariant, based on the eta invariant of a Dirac operator, to distinguish connected components. The standard method of calculation involves extending the metric to one of positive scalar curvature on a spin bounding manifold. We generalize this method to spinc bounding orbifolds and apply it utilizing almost free isometric circle actions on the examples. This generalization has wide applications to questions about moduli spaces of metrics and diffeomorphism classifications.