Abstract

Cheeger-Fukaya-Gromov’s N-structure describes the phenomena on “collapsing implies nilpotent symmetry under bounded sectional curvature”. But such N-structure does not exist on those manifolds with bounded Ricci curvature in general, e.g., Ricci-flat K3 surfaces. We will give a survey on a program that is to find sufficient and necessary conditions for the existence of N-structure under bounded or lower bounded Ricci curvature. In particular, we prove that an admissible N-structure exists under bounded Ricci curvature if the local orthonormal frame bundle is close to a regular limit space with full rank local fundamental group.

The venue is Wencui Building I202, Liangxiang Campus, BIT (北京理工大学良乡校区，文萃楼I202). Those wishing to participate should contact Prof. Chao Qian (6120150035@bit.edu.cn) for the entrance permission to the campus.