2009/03/31 by D. Kotschick
Mathematics · #Biology #Characterization (materials science) #Curvature #Ecology #Genus #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Mathematical optimization #Mathematics #Negative curvature #Optimal control #Physics #Point processes and geometric inequalities #Pontryagin's minimum principle #Pure mathematics #Scalar curvature #Sectional curvature #Signature (topology) #math.DG #math.GT #msc:53C21 #msc:53C23 #msc:57R20 #msc:57R75
paper · pdf · doi:10.1515/crelle.2010.068
published as J. reine angew. Math. 646 (2010), 135-140 · 7 pages; this version is longer than the published one, since it contains some additional material
openalex publication_date 2010/01/01 · arxiv created 2011/09/04 · arxiv updated 2011/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 boundedness result for the signature yields a new characterization of the L -genus.