FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

Let M be a closed n-manifold of positive sectional curvature. Assume that M admits an effective isometrical T1× Zpk-action with p prime. The main result of the article n＋1 for n 〉 5, then there exists a positive constant p（n）, is that ifk=lforn=3or k〉 n＋1/4 for n≥5,then there exists a positive const...

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Bibliographic Details
Published in:Acta mathematica scientia 2010, Vol.30 (1), p.203-207
Main Author: 王雨生
Format: Article
Language:English
Subjects:
53C20
Abel群
Curvature
Curved
fundamental groups
group actions
Manifolds
Mathematical analysis
positive sectional curvature
哥德堡
基本群
截面曲率
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Summary:Let M be a closed n-manifold of positive sectional curvature. Assume that M admits an effective isometrical T1× Zpk-action with p prime. The main result of the article n＋1 for n 〉 5, then there exists a positive constant p（n）, is that ifk=lforn=3or k〉 n＋1/4 for n≥5,then there exists a positive constant p（n）,depending only on n, such that π1 （M） is cyclic if p ≥ p（n）.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(10)60037-9