2012/01/09 by Boris Botvinnik, Botvinnik, Boris, Mohammed Larbi Labbi +2
Mathematics · #53C20 #57R90 (Primary) 81T30 (Secondary) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:53C20 #msc:57R90 #msc:81T30
paper · pdf · doi:10.48550/arxiv.1201.1849
This is a revised version where some typos are corrected, one argument in the proof of proposition 3.7 revised and the results are unchanged
openalex publication_date 2012/01/09 · arxiv created 2013/01/05 · arxiv updated 2013/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study and in some cases classify highly connected manifolds which admit a Riemannian metric with positive p-curvature. The p-curvature was defined and studied by the second author. It turns out that positivity of p-curvature could be preserved under surgeries of codimension at least p+3. This gives a key to reduce a geometrical classification problem to a topological one, in terms of relevant bordism groups and index theory. In particular, we classify 3-connected manifolds with positive 2-curvature in terms of the spin and string bordism groups, and by means of α-invariant and Witten genus ϕW. Here we use results of Dessai, which provide appropriate generators of the rational string bordism ring in terms of "geometric \Ca P2-bundles", where the Cayley projective plane \Ca P2 is a fiber and the structure group is F4 which is the isometry group of the standard metric on \Ca P2.