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)

 
 

 

The set of balanced orbits of maps of $ S\sp 1$ and $ S\sp 3$ actions


Author: Jan Jaworowski
Journal: Proc. Amer. Math. Soc. 98 (1986), 158-162
MSC: Primary 57S10; Secondary 55M20, 55N25, 55R40
DOI: https://doi.org/10.1090/S0002-9939-1986-0848895-4
MathSciNet review: 848895
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that the group $ G = {S^1}$ or $ G = {S^3}$ acts freely on a space $ X$ and on a representation space $ V$ for $ G$. Let $ f:X \to V$. The paper studies the size of the subset of $ X$ consisting of orbits over which the average of $ f$ is zero. The result can be viewed as an extension of the Borsuk-Ulam theorem.


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

  • [1] P. E. Conner and E. E. Floyd, Fixed point free involutions and equivariant maps, Bull. Amer. Math. Soc. 66 (1960), 416-441. MR 0163310 (29:613)
  • [2] A. Dold, Simple proofs of some Borsuk-Ulam results (Proc. Northwestern Homotopy Theory Conf., Evanston, Ill., 1982), Contemp. Math., vol. 19, Amer. Math. Soc., Providence, R.I., 1983, pp. 65-70. MR 711043 (85e:55003)
  • [3] E. R. Fadell and P. H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), 139-174. MR 0478189 (57:17677)
  • [4] E. R. Fadell, S. Y. Husseini and P. H. Rabinowitz, Borsuk-Ulam theorems for arbitrary $ {S^1}$ actions and applications, Trans. Amer. Math. Soc. 274 (1982), 345-360. MR 670937 (84b:55001)
  • [5] A. Liulevicius, Borsuk-Ulam theorems for spherical space forms (Proc. Northwestern Homotopy Theory Conf., Evanston, Ill., 1982), Contemp. Math., vol. 19, Amer. Math. Soc., Providence, R.I., 1983, pp. 189-192. MR 711052 (84j:55008)
  • [6] N. Steenrod, The topology of fibre bundles, Princeton University Press, Princeton, N.J., 1951. MR 0039258 (12:522b)
  • [7] C. T. Yang, On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson. II, Ann. of Math. (2) 62 (1955), 271-283. MR 0072470 (17:289e)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57S10, 55M20, 55N25, 55R40

Retrieve articles in all journals with MSC: 57S10, 55M20, 55N25, 55R40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0848895-4
Keywords: Average, equivariant map, equivariant cohomology, characteristic class, index
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society