$ {\mathrm{Spin}}^{q}$ manifolds and $ {S}^{1}$ actions

Haydeé Herrera; Rafael Herrera

doi:10.1016/j.crma.2007.05.019

Topology

{Spin}^{q}

manifolds and

S^{1}

actions

Presented by: Étienne Ghys

Haydeé Herrera ¹; Rafael Herrera ²

¹ Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA
² Centro de Investigación en Matemáticas, A. P. 402, Guanajuato, Gto., C.P. 36000, Mexico

Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 35-38

Abstract (Original language)
Résumé

We prove a vanishing theorem for ${Spin}^{q}$ manifolds admitting $S^{1}$ actions, generalizing those of Atiyah and Hirzebruch for Spin manifolds and Hattori for ${Spin}^{c}$ manifolds. We also prove a vanishing theorem for almost quaternionic manifolds with compatible circle actions.

On montre un théorème d'annulation pour les variétés ${Spin}^{q}$ qui admettent des actions de $S^{1}$ , ce qui généralise le théorème d'Atiyah et de Hirzebruch pour les variétés de Spin et celui de Hattori pour les variétés ${Spin}^{c}$ . De plus, on montre un théorème d'annulation pour les variétés presque quaternionienne qui admettent des actions de $S^{1}$ compatibles.

Received: 2007-03-23
Accepted: 2007-05-24
Published online: 2007-06-27

DOI: 10.1016/j.crma.2007.05.019

Author's affiliations:

Haydeé Herrera ¹; Rafael Herrera ²

¹ Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA
² Centro de Investigación en Matemáticas, A. P. 402, Guanajuato, Gto., C.P. 36000, Mexico

@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},
     year = {2007},
     publisher = {Elsevier},
     volume = {345},
     number = {1},
     doi = {10.1016/j.crma.2007.05.019},
     language = {en},
}

TY  - JOUR
AU  - Haydeé Herrera
AU  - Rafael Herrera
TI  - $ {\mathrm{Spin}}^{q}$ manifolds and $ {S}^{1}$ actions
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 35
EP  - 38
VL  - 345
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2007.05.019
LA  - en
ID  - CRMATH_2007__345_1_35_0
ER  -

%0 Journal Article
%A Haydeé Herrera
%A Rafael Herrera
%T $ {\mathrm{Spin}}^{q}$ manifolds and $ {S}^{1}$ actions
%J Comptes Rendus. Mathématique
%D 2007
%P 35-38
%V 345
%N 1
%I Elsevier
%R 10.1016/j.crma.2007.05.019
%G en
%F CRMATH_2007__345_1_35_0

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

References
Cited by

[1] M. Atiyah; F. Hirzebruch Spin-manifolds and group actions, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. 18-28

[2] M.F. Atiyah; I.M. Singer The index of elliptic operators. III, Ann. of Math. (2), Volume 87 (1968), pp. 546-604

[3] W. Fulton; S. Lang Riemann–Roch Algebra, Fundamental Principles of Mathematical Sciences, vol. 277, Springer-Verlag, New York, 1985 (x+203 pp)

[4] A. Hattori ${Spin}^{c}$ -structures and $S^{1}$ -actions, Invent. Math., Volume 48 (1978) no. 1, pp. 7-31

[5] H.B. Lawson; M. Michelsohn Spin Geometry, Princeton Mathematical Series, vol. 38, Princeton University Press, Princeton, NJ, 1989 (xii+427 pp)

[6] M. Nagase ${Spin}^{q}$ structures, J. Math. Soc. Japan, Volume 47 (1995) no. 1, pp. 93-119

Cited by Sources:

Comments - Policy