Discrete symmetry, toral symmetry and the Euler characteristic of manifolds

Papadima, Ştefan

doi:10.1090/S0002-9939-1988-0943092-8

Discrete symmetry, toral symmetry and the Euler characteristic of manifolds
HTML articles powered by AMS MathViewer

by Ştefan Papadima PDF

Proc. Amer. Math. Soc. 103 (1988), 612-614 Request permission

Abstract:

We consider a closed manifold $M$ and establish various connections between its Euler characteristic and certain numerical invariants defined so as to measure the abundance of free discrete (respectively rationally free toral) group actions supported by $M$.

References

Christopher Allday and Stephen Halperin, Lie group actions on spaces of finite rank, Quart. J. Math. Oxford Ser. (2) 29 (1978), no. 113, 63–76. MR 501046, DOI 10.1093/qmath/29.1.63
Marc Aubry and Jean-Michel Lemaire, Sommes connexes fibrées en cercles, Bull. Soc. Math. France 113 (1985), no. 4, 459–462 (French, with English summary). MR 850777

On periodic maps on certain

P. E. Conner and Frank Raymond, Manifolds with few periodic homeomorphisms, Proceedings of the Second Conference on Compact Transformation Groups (Univ. Massachusetts, Amherst, Mass., 1971) Lecture Notes in Math., Vol. 299, Springer, Berlin, 1972, pp. 1–75. MR 0358835
F. B. Fuller, The existence of periodic points, Ann. of Math. (2) 57 (1953), 229–230. MR 52764, DOI 10.2307/1969856
Stephen Halperin, Rational homotopy and torus actions, Aspects of topology, London Math. Soc. Lecture Note Ser., vol. 93, Cambridge Univ. Press, Cambridge, 1985, pp. 293–306. MR 787835
Wu-yi Hsiang, Cohomology theory of topological transformation groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 85, Springer-Verlag, New York-Heidelberg, 1975. MR 0423384
James E. Humphreys, Linear algebraic groups, Graduate Texts in Mathematics, No. 21, Springer-Verlag, New York-Heidelberg, 1975. MR 0396773
Peter Löffler and Martin Raußen, Symmetrien von Mannigfaltigkeiten und rationale Homotopietheorie, Math. Ann. 271 (1985), no. 4, 549–576 (German). MR 790115, DOI 10.1007/BF01456134
Ştefan Papadima, Rigidity properties of compact Lie groups modulo maximal tori, Math. Ann. 275 (1986), no. 4, 637–652. MR 859335, DOI 10.1007/BF01459142
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1