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SUMMARY:Good complexifications of nonnegatively curved manifolds
DTSTART:20261007T133000Z
DTEND:20261007T144500Z
DTSTAMP:20261015T013000Z
UID:indico-event-17491@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ethan Peng (IPP/formerly at IPAM)\n\n\n\nA closed ma
 nifold 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 manif
 olds\, including classical ones (spheres\, RP2\, homogeneous spaces\, Chee
 ger manifolds)\, as well as a class of closed Riemannian manifolds with no
 n-negative sectional curvature constructed by B. Totaro using plumbing tec
 hniques. We will also discuss topological constraints on closed manifolds 
 admitting a good complexification\, such as the classical non-negativity o
 f its Euler characteristic\, and vanishing of some Betti numbers and Pontr
 yagin numbers as proved by Totaro. An effort will be made to explain how t
 he curvature constraints interplay with the algebro-geometric aspects. If 
 time permits\, we will also discuss how good complexifications pass to quo
 tients by nice group actions\, giving ways to "algebraicize" various famil
 iar manifolds.\n \n\n\n \n\nhttps://indico.math.cnrs.fr/event/17491/
LOCATION:Salle Pierre Grisvard (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/17491/
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