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An HP2-bundle over S4 with nontrivial A-genus b

Accepted version
Peer-reviewed

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Type

Article

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Authors

Krannich, M 
Kupers, A 
Randal-Williams, Oscar  ORCID logo  https://orcid.org/0000-0002-7479-2878

Abstract

We explain the existence of a smooth HP2-bundle over S4 whose total space has nontrivial A^-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.

Description

Keywords

math.AT, math.AT, math.DG, math.GT, 57R20, 55R40, 57R22, 58D17

Journal Title

Comptes Rendus Mathematique

Conference Name

Journal ISSN

1631-073X
1778-3569

Volume Title

359

Publisher

Cellule MathDoc/Centre Mersenne

Rights

All rights reserved
Sponsorship
European Research Council (756444)
Leverhulme Trust (PLP-2017-017)
ERC, Leverhulme Trust