Good complexifications of nonnegatively curved manifolds

par Ethan Peng (IPP/formerly at IPAM)

mercredi 7 oct. 2026, 15:30 → 16:45 Europe/Paris

Salle Pierre Grisvard (IHP)

A closed manifold M admits a good complexification if it is diffeomorphic to the set of real points of a real affine variety X such that the embedding X(R) -> X(C) is a homotopy equivalence. We will give examples of such closed manifolds, including classical ones (spheres, RP², homogeneous spaces, Cheeger manifolds), as well as a class of closed Riemannian manifolds with non-negative sectional curvature constructed by B. Totaro using plumbing techniques. We will also discuss topological constraints on closed manifolds admitting a good complexification, such as the classical non-negativity of its Euler characteristic, and vanishing of some Betti numbers and Pontryagin numbers as proved by Totaro. An effort will be made to explain how the curvature constraints interplay with the algebro-geometric aspects. If time permits, we will also discuss how good complexifications pass to quotients by nice group actions, giving ways to "algebraicize" various familiar manifolds.