Pontryagin numbers and nonnegative curvature

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.Comment: 7 pages; this version is longer than the published one, since it contains some additional materia