Pontryagin numbers and nonnegative curvature

TL;DR

This paper demonstrates that certain linear combinations of Pontryagin numbers are unbounded on manifolds with nonnegative sectional curvature, providing new insights into the relationship between curvature and topological invariants.

Contribution

It establishes that only multiples of the signature remain bounded among Pontryagin numbers in nonnegative curvature manifolds, leading to a new characterization of the L-genus.

Findings

Unboundedness of non-multiple Pontryagin numbers on nonnegative curvature manifolds

Connection between Pontryagin numbers and the signature in curvature contexts

New characterization of the L-genus based on curvature constraints

Abstract

We prove that any rational linear combination of Pontryagin numbers that is not a multiple of the signature is unbounded on connected closed oriented manifolds of nonnegative sectional curvature. Combining our result with Gromov's finiteness result for the signature yields a new characterization of the L-genus.