8-9 November 2018
University of Fribourg, Switzerland
Europe/Berlin timezone

$\mathop{Spin}^c$ Dirac operators and the Kreck-Stolz s invariant.

9 Nov 2018, 10:40
University of Fribourg, Switzerland

University of Fribourg, Switzerland


Jackson Goodman (University of Pennsylvania)


We use the $\mathop{Spin}^c$ Dirac operator to generalize a formula of Kreck and Stolz for the s invariant of $S^1$ invariant metrics with positive scalar curvature. We then apply it to show that the moduli spaces of metrics with nonnegative sectional curvature on certain 7-manifolds have infinitely many path components. These include certain positively curved Eschenburg and Aloff-Wallach spaces. Furthermore, we use a $\mathop{Spin}^c$ version of the s invariant to discuss moduli spaces of metrics of positive scalar and twisted scalar curvature on $\mathop{Spin}^c$ manifolds.

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