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.
Nous expliquons l’existence d’un fibré différentiel de base et fibre , dont l’espace total est de -genre non-trivial. En combinant ce resultat avec un argument de Hitchin, ceci répond à une question de Schick et implique que l’espace de métriques riemanniennes de courbure sectionnelle positive sur une variété fermée peut avoir des groupes d’homotopie rationnelle supérieures non-triviaux.
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Manuel Krannich 1; Alexander Kupers 2; Oscar Randal-Williams 1
@article{CRMATH_2021__359_2_149_0, author = {Manuel Krannich and Alexander Kupers and Oscar Randal-Williams}, title = {An $\protect \text{HP}^2$-bundle over $\protect \text{S}^4$ with nontrivial {\^A-genus}}, journal = {Comptes Rendus. Math\'ematique}, pages = {149--154}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {2}, year = {2021}, doi = {10.5802/crmath.156}, language = {en}, }
TY - JOUR AU - Manuel Krannich AU - Alexander Kupers AU - Oscar Randal-Williams TI - An $\protect \text{HP}^2$-bundle over $\protect \text{S}^4$ with nontrivial Â-genus JO - Comptes Rendus. Mathématique PY - 2021 SP - 149 EP - 154 VL - 359 IS - 2 PB - Académie des sciences, Paris DO - 10.5802/crmath.156 LA - en ID - CRMATH_2021__359_2_149_0 ER -
%0 Journal Article %A Manuel Krannich %A Alexander Kupers %A Oscar Randal-Williams %T An $\protect \text{HP}^2$-bundle over $\protect \text{S}^4$ with nontrivial Â-genus %J Comptes Rendus. Mathématique %D 2021 %P 149-154 %V 359 %N 2 %I Académie des sciences, Paris %R 10.5802/crmath.156 %G en %F CRMATH_2021__359_2_149_0
Manuel Krannich; Alexander Kupers; Oscar Randal-Williams. An $\protect \text{HP}^2$-bundle over $\protect \text{S}^4$ with nontrivial Â-genus. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 149-154. doi : 10.5802/crmath.156. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.156/
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