COMPACT LIE GROUP ACTIONS ON ASPHERICAL $A_k(\pi)$-MANIFOLDS

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Published: Dec 1, 1993
DOI: https://doi.org/10.5556/j.tkjm.24.1993.4511
Keywords:
actions of compact Lie groups aspherical Ak(π)-manifold semisimple degree of symmetry

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DINGYI TANG
Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, U. S. A.

Abstract




Let M be an aspberical $A_k(\pi)$-manifold and $\pi'$-torsion-free, where $\pi'$ is some quotient group of $\pi$. We prove that


(1) Suppose the Eu­ler characteristic $\mathcal{X}(M) \neq 0$ and $G$ is compact Lie group acting effectively on $M$, then $G$ is finite group


(2) The semisimple degree of symmetry of $M$ $N_T^s \le (n - k)(n - k+1)/2$. We also unity many well-known results with simpler proofs.




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How to Cite
TANG, D. (1993). COMPACT LIE GROUP ACTIONS ON ASPHERICAL $A_k(\pi)$-MANIFOLDS. Tamkang Journal of Mathematics, 24(4), 395–403. https://doi.org/10.5556/j.tkjm.24.1993.4511
Issue
Vol. 24 No. 4 (1993)
Section
Papers
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