Group actions on aspherical $A_{k}(N)$-manifolds with nonzero Euler characteristics
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Abstract:
By an aspherical ${A_k}(N)$-manifold, we mean a compact manifold $M$ together with a map $f$ from $M$ into an aspherical complex $N$ such that ${f^*}$: ${H^k}(N;Q) \to {H^k}(M;Q)$ is nontrivial. In this paper we study the fixed point set, degree of symmetry, semisimple degree of symmetry and torus degree of symmetry of $M$ with the Euler characteristic of $M$ nonzero.References
- Armand Borel, Seminar on transformation groups, Annals of Mathematics Studies, No. 46, Princeton University Press, Princeton, N.J., 1960. With contributions by G. Bredon, E. E. Floyd, D. Montgomery, R. Palais. MR 0116341
- Glen E. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, Vol. 46, Academic Press, New York-London, 1972. MR 0413144
- Dan Burghelea and Reinhard Schultz, On the semisimple degree of symmetry, Bull. Soc. Math. France 103 (1975), no. 4, 433–440 (English, with French summary). MR 397756, DOI 10.24033/bsmf.1810
- P. E. Conner and D. Montgomery, Transformation groups on a $K(\pi ,\,1)$. I, Michigan Math. J. 6 (1959), 405–412. MR 123333
- P. E. Conner and Frank Raymond, Actions of compact Lie groups on aspherical manifolds, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp. 227–264. MR 0271958
- Harold Donnelly and Reinhard Schultz, Compact group actions and maps into aspherical manifolds, Topology 21 (1982), no. 4, 443–455. MR 670746, DOI 10.1016/0040-9383(82)90022-2
- 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, DOI 10.1007/978-3-642-66052-8
- Hsu-tung Ku, A generalization of the Conner inequalities, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 401–414. MR 0257270
- Hsü Tung Ku and Mei Chin Ku, Group actions on $A_{k}$-manifolds, Trans. Amer. Math. Soc. 245 (1978), 469–492. MR 511424, DOI 10.1090/S0002-9947-1978-0511424-9
- Hsü Tung Ku and Mei Chin Ku, Group actions on aspherical $A_{k}(N)$-manifolds, Trans. Amer. Math. Soc. 278 (1983), no. 2, 841–859. MR 701526, DOI 10.1090/S0002-9947-1983-0701526-8
- H. T. Ku, L. N. Mann, J. L. Sicks, and J. C. Su, Degree of symmetry of a homotopy real projective space, Trans. Amer. Math. Soc. 161 (1971), 51–61. MR 282377, DOI 10.1090/S0002-9947-1971-0282377-X
- L. N. Mann, Gaps in the dimensions of transformation groups, Illinois J. Math. 10 (1966), 532–546. MR 200387
- Shing Tung Yau, Remarks on the group of isometries of a Riemannian manifold, Topology 16 (1977), no. 3, 239–247. MR 448379, DOI 10.1016/0040-9383(77)90004-0
- Richard Schoen and Shing Tung Yau, Compact group actions and the topology of manifolds with nonpositive curvature, Topology 18 (1979), no. 4, 361–380. MR 551017, DOI 10.1016/0040-9383(79)90026-0
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 459-462
- MSC: Primary 57S10; Secondary 57S15, 57S25
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728369-X
- MathSciNet review: 728369