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Proceedings of the American Mathematical Society

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



Discrete symmetry, toral symmetry and the Euler characteristic of manifolds

Author: Ştefan Papadima
Journal: Proc. Amer. Math. Soc. 103 (1988), 612-614
MSC: Primary 57S17; Secondary 57S15
MathSciNet review: 943092
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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$.

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  • [1] C. Allday and S. Halperin, Lie group actions on spaces of finite rank, Quart. J. Math. Oxford Ser. 29 (1978), 63-76. MR 0501046 (58:18510)
  • [2] M. Aubry and J.-M. Lemaire, Sommes connexes fibrées en cercles, Bull. Soc. Math. France 113 (1985), 459-462. MR 850777 (87h:57032)
  • [3] A. Borel, On periodic maps on certain $ K(\pi ,1)$, Collected Papers, vol. III, Springer-Verlag, 1983, pp. 57-60.
  • [4] P. E. Conner and F. Raymond, Manifolds with few periodic homeomorphisms, Proc. Second Conf. on Compact Transformation Groups, Part II, Lecture Notes in Math., vol. 299, Springer-Verlag, Berlin and New York, 1972, pp. 1-75. MR 0358835 (50:11294)
  • [5] F. B. Fuller, The existence of periodic points, Ann. of Math. (2) 57 (1953), 229-230. MR 0052764 (14:669f)
  • [6] S. Halperin, Rational homotopy and torus actions, Aspects of Topology, Mem. H. Dowker, London Math. Soc. Lecture Note Ser. 93, 1985, pp. 293-306. MR 787835 (87d:55001)
  • [7] W.-Y. Hsiang, Cohomology theory of topological transformation groups, Springer-Verlag, 1975. MR 0423384 (54:11363)
  • [8] J. E. Humphreys, Linear algebraic groups, Springer-Verlag, 1975. MR 0396773 (53:633)
  • [9] P. Löffler and M. Raussen, Symmetrien von Mannigfaltigkeiten und Rationale Homotopietheorie, Math. Ann. 271 (1985), 549-576. MR 790115 (86i:57043)
  • [10] S. Papadima, Rigidity properties of compact Lie groups modulo maximal tori, Math. Ann. 275 (1986), 637-652. MR 859335 (88b:53063)
  • [11] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)

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Keywords: Euler characteristic, free (rationally free) action
Article copyright: © Copyright 1988 American Mathematical Society

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