Almost Nonnegative Ricci curvature and new vanishing theorems for genera

TL;DR

This paper establishes new vanishing theorems for various genera and the Euler characteristic in spaces with almost nonnegative Ricci curvature and infinite fundamental group, extending classical results to broader geometric contexts.

Contribution

It introduces novel vanishing theorems for several genera and Euler characteristic under almost nonnegative Ricci curvature, including Alexandrov spaces.

Findings

Vanishing of Todd, , elliptic, and Witten genera under specified conditions.

Proved a vanishing theorem for Euler characteristic in Alexandrov spaces.

Extended classical vanishing results to spaces with almost nonnegative Ricci curvature.

Abstract

We derive several vanishing theorems for genera under almost nonnegative Ricci curvature and infinite fundamental group, which includes Todd genus, $\widehat{A}$-genus, elliptic genera and Witten genus. A vanishing theorem of Euler characteristic number for almost nonnegatively curved Alexandrov spaces is also proved.