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Xiaochun Rong: Lectures

April 11, 2018
TITLE: Collapsed manifolds with Ricci local bounded covering geometry

ABSTRACT: Collapsed manifolds with local bounded covering geometry (i.e., sectional curvature bounded in absolute value) has been well-studied; the basic discovery by Cheeger-Fukaya-Gromov is the existence of a compatible local nilpotent symmetry structures whose orbits point to all collapsed directions.

In this talk, we will report an on-going work in generalizing the structural result to collapsed manifolds with (partially) local Ricci bounded covering geometry; which may contain a large class of collapsed Calabi-Yau manifolds and Ricci flat manifolds with special holonomy. Our construction of local nilpotent symmetry structures does not reply on the work of Cheeger-Fukaya-Gromov; which gives alternative approach to the structural result.

Slides of lecture