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Jonathan Wermelinger

Publications and source records attributed to Jonathan Wermelinger.

3 recordsLinked to original sources
arXiv2022

The moduli Space of nonnegatively curved metrics on quotients of $S^2\times S^3$ by involutions

We show that for an orientable non-spin manifold with fundamental group $\mathbb{Z}_2$ and universal cover $S^2\times S^3,$ the moduli space of metrics of nonnegative sectional curvature has infinitely many path components. The representatives of the components are quotients of the standard metric on $S^3\times S^3$ or metrics on Brieskorn varieties previously constructed using cohomogeneity one actions. The components are distinguished using the relative $\eta$ invariant of the spin$^c$ Dirac operator computed by means of a Lefschetz fixed point theorem.

math.DG↗
arXiv2020

Moduli space of non-negative sectional or positive Ricci curvature metrics on sphere bundles over spheres and their quotients

We show that the moduli space of positive Ricci curvature metrics on all the total spaces of $S^7$-bundles over $S^8$ which are rational homology spheres has infinitely many path components. Furthermore, we carry out the diffeomorphism classification of quotients of Milnor spheres by a certain involution and show that the moduli space of metrics of non-negative sectional on them has infinitely many path components. Finally, a diffeomorphism finiteness result is obtained on quotients of Shimada spheres by the same type of involution and we show that for the types that can be expressed by an infinite family of manifolds, the moduli space of positive Ricci curvature metrics has infinitely many path components.

math.DG↗