An $HP^2$-bundle over $S^4$ with nontrivial $\hat{A}$-genus
Algebraic Topology
2022-02-10 v2 Differential Geometry
Geometric Topology
Abstract
We explain the existence of a smooth -bundle over whose total space has nontrivial -genus. Combined with an argument going back to Hitchin, this answers a question of Schick and implies that the space of Riemannian metrics of positive sectional curvature on a closed manifold can have nontrivial higher rational homotopy groups.
Cite
@article{arxiv.2007.15062,
title = {An $HP^2$-bundle over $S^4$ with nontrivial $\hat{A}$-genus},
author = {Manuel Krannich and Alexander Kupers and Oscar Randal-Williams},
journal= {arXiv preprint arXiv:2007.15062},
year = {2022}
}
Comments
5 pages, to appear in Comptes Rendus. Math\'ematique