A note on the Petersen-Wilhelm conjecture

González-Álvaro, David; Radeschi, Marco

doi:10.1090/proc/14070

A note on the Petersen-Wilhelm conjecture
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by David González-Álvaro and Marco Radeschi PDF

Proc. Amer. Math. Soc. 146 (2018), 4447-4458 Request permission

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.

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