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Four-dimensional Cohomogeneity one Ricci flow and Nonnegative sectional curvature

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Speaker: 
Anusha Mangala Krishnan
Affiliation: 
University of Pennsylvania
Date: 
Mon, 2017-04-03 17:00 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Young Women in Geometry

We study the Ricci flow on $4$-manifolds admitting a cohomogeneity one group action, i.e. an isometric group action such that the orbit space $M/G$ is $1$-dimensional. We use this to demonstrate the first examples of 4-manifolds having nonnegative sectional curvature which under the Ricci flow, immediately acquire some negatively curved 2-planes. In particular, we show that $S^4$, $\mathbb{C}P^2$, $S^2\times S^2$ and $\mathbb{C}P^2 \# \overline{\mathbb{C}P^2}$ admit such metrics. This talk is based on joint work with Renato G. Bettiol.

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