Collapsing with a lower bound on the curvature operator

TL;DR

This paper extends Cheeger-Gromov's results by defining fibered F-structures and analyzing collapse scenarios with a lower curvature operator bound, broadening understanding of geometric collapse under curvature constraints.

Contribution

It introduces fibered F-structures and generalizes collapse results to settings with a lower curvature operator bound, expanding the theoretical framework.

Findings

Extended Cheeger-Gromov results to lower curvature bounds

Defined fibered F-structures for collapse analysis

Provided new insights into geometric collapse scenarios

Abstract

Cheeger and Gromov showed that F-structures are related to collapse with a double-sided curvature bound. We define fibered F-structures and extend some of the Cheeger-Gromov results to the setting of collapse with a lower bound on the curvature operator.