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 A. Borel, On periodic maps on certain $K(\pi ,1)$, Collected Papers, vol. III, Springer-Verlag, 1983, pp. 57-60.
- 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
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 612-614
- MSC: Primary 57S17; Secondary 57S15
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943092-8
- MathSciNet review: 943092