Unbounded Pontryagin numbers on nonnegatively curved spin manifolds

TL;DR

This paper demonstrates that certain Pontryagin number combinations are unbounded on nonnegatively curved spin manifolds unless they factor through the universal elliptic genus, revealing new constraints on geometric invariants.

Contribution

It establishes a new unboundedness result for Pontryagin numbers on nonnegatively curved spin manifolds, linking topological invariants to geometric curvature conditions.

Findings

Pontryagin numbers are unbounded unless factoring through the universal elliptic genus.

Provides a characterization of which topological invariants are bounded in nonnegative curvature.

Connects algebraic topology with geometric curvature constraints.

Abstract

We prove that any rational linear combination of Pontryagin numbers that does not factor through the universal elliptic genus is unbounded on connected closed spin manifolds of nonnegative sectional curvature.