We prove a vanishing theorem for manifolds admitting actions, generalizing those of Atiyah and Hirzebruch for Spin manifolds and Hattori for manifolds. We also prove a vanishing theorem for almost quaternionic manifolds with compatible circle actions.
On montre un théorème d'annulation pour les variétés qui admettent des actions de , ce qui généralise le théorème d'Atiyah et de Hirzebruch pour les variétés de Spin et celui de Hattori pour les variétés . De plus, on montre un théorème d'annulation pour les variétés presque quaternionienne qui admettent des actions de compatibles.
Accepted:
Published online:
Haydeé Herrera 1; Rafael Herrera 2
@article{CRMATH_2007__345_1_35_0, author = {Hayde\'e Herrera and Rafael Herrera}, title = {$ {\mathrm{Spin}}^{q}$ manifolds and $ {S}^{1}$ actions}, journal = {Comptes Rendus. Math\'ematique}, pages = {35--38}, publisher = {Elsevier}, volume = {345}, number = {1}, year = {2007}, doi = {10.1016/j.crma.2007.05.019}, language = {en}, }
Haydeé Herrera; Rafael Herrera. $ {\mathrm{Spin}}^{q}$ manifolds and $ {S}^{1}$ actions. Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 35-38. doi : 10.1016/j.crma.2007.05.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.019/
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