A note on the Petersen-Wilhelm conjecture

2017/06/01 by David González-Álvaro, Marco Radeschi, González-Álvaro, David +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1706.00366

11 pages

arxiv created 2017/06/01 · arxiv updated 2017/06/02

Abstract

In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontrivial, the dimension of the base is greater than the dimension of the fiber. Together with previous results, this proves the Petersen-Wilhelm Conjecture for all the known compact manifolds with positive curvature.

Related

• The Petersen--Wilhelm conjecture on principal bundles
• An intrinsic curvature condition for submersions over Riemannian manifolds
• A generalized Frankel conjecture via the Yang-Mills flow
• The Coarse Geometric ℓ^p-Novikov Conjecture for Subspaces of Non-positively Curved Manifolds
• Symmetries of Eschenburg spaces and the Chern problem