Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$ \alpha$-invariant and $ S\sp 1$ actions


Author: Kaoru Ono
Journal: Proc. Amer. Math. Soc. 112 (1991), 597-600
MSC: Primary 58G10; Secondary 55N15, 57R15
DOI: https://doi.org/10.1090/S0002-9939-1991-1043417-1
MathSciNet review: 1043417
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If a closed spin manifold admits an $ {S^1}$ action of odd type, then its $ \alpha $-invariant vanishes.


References [Enhancements On Off] (What's this?)

  • [A-B-S] M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), 3-38. MR 0167985 (29:5250)
  • [A-H] M. F. Atiyah and F. Hirzebruch, Spin manifolds and group actions, Essays in Topology and Related Topics, Springer-Verlag, Berlin, 1970, pp. 18-28. MR 0278334 (43:4064)
  • [A-S] M. F. Atiyah and I. M. Singer, Index theory for skew adjoint Fredholm operators, Publ. Math. IHES 37 (1969) 5-26. MR 0285033 (44:2257)
  • [A-S V] -, The index of elliptic operators $ V$ Ann. Math. 93 (1971), 139-149. MR 0279834 (43:5555)
  • [H] N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1-55. MR 0358873 (50:11332)
  • [L-S] P. S. Landweber and R. E. Stong, Circle actions on spin manifolds and characteristic numbers, Topology 27 (1988), 145-161. MR 948178 (90a:57040)
  • [L] A. Lichnerowicz, Spineurs harmoniques, C.R. Acad. Sci. Paris Sér. A-B 257 (1963), 7-9. MR 0156292 (27:6218)
  • [M] J. Milnor, Remarks concerning spin manifolds, Differential and Combinatorial Topology: A Symposium in Honor of Marston Morse, Princeton Univ. Press, Princeton, NJ, 1965, pp. 55-62. MR 0180978 (31:5208)
  • [O] S. Ochanine, Genres elliptiques equivariants, Elliptic Curves and Modular Forms in Algebraic Topology (P. S. Landweber, ed.), Lecture Notes in Math., vol. 1326, Springer-Verlag, Berlin, 1988, pp. 107-122. MR 970284

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G10, 55N15, 57R15

Retrieve articles in all journals with MSC: 58G10, 55N15, 57R15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1043417-1
Keywords: $ \alpha $-invariant, Dirac operator
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society