Open AccessCOMPACT LIE GROUP ACTIONS ON ASPHERICAL $A_k(\pi)$-MANIFOLDS
Author(s) -
Dingyi Tang
Publication year - 1993
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.24.1993.4511
Subject(s) - mathematics , quotient , lie group , pi , torsion (gastropod) , pure mathematics , group (periodic table) , mathematical proof , combinatorics , geometry , physics , quantum mechanics , medicine , surgery
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.