Highly connected manifolds of positive $p$-curvature

Details Highly connected manifolds of positive $p$-curvature Highly connected manifolds of positive $p$-curvature

2012-01-09

arxiv.org/abs/1201.1849v1

Mathematics

Differential Geometry

21 pages

Scientific paper

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 $\alpha$-invariant and Witten genus $\phi_W$. Here we use results of Dessai, which provide appropriate generators of the rational string bordism ring in terms of "geometric $\Ca P^2$-bundles", where the Cayley projective plane $\Ca P^2$ is a fiber and the structure group is $F_4$ which is the isometry group of the standard metric on $\Ca P^2$.

Affiliated with

Also associated with

No associations

Rating

Highly connected manifolds of positive $p$-curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Highly connected manifolds of positive $p$-curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Highly connected manifolds of positive $p$-curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643715