The Gauss-Bonnet inequality beyond aspherical conjecture
Date:
Friday, 14 July, 2023 - 09:00 - 12:00
Venue:
https://cuhk.zoom.us/j/95988240027 (Passcode is six numbers: five-four-nine-seven-zero-eight)
Seminar Type:
CUHK-CUNY-2023 Compactness and Scalar Curvature Workshop
Speaker Name:
Dr. Jintian ZHU
Affiliation:
Peking University
Abstract:
In this talk, I plan to first review the topic of largeness behind the aspherical conjecture, and
then focus on the following Gauss-Bonnet inequality beyond the aspherical conjecture: if the
universal covering of a closed manifold with nonnegative scalar curvature has ``homological
dimension no greater than two'', then either it is flat or its Gauss-Bonnet quantity is no
greater than $8\pi$, where the Gauss-Bonnet quantity is the infimum of ambient-scalarcurvature-
integral over homotopically non-trivial two-spheres. I'll also mention my conjecture
on Gauss-Bonnet inequality with boundary following the view of geometry-over-topology
principle. See https://arxiv.org/abs/2206.07955.
Poster:
