数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 203-207.doi: 10.1016/S0252-9602(10)60037-9

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

 WANG Yu-Sheng   

  1. School of Mathematical Sciences (&|Laboratory of Mathematics and Complex Systems), Beijing Normal University, |Beijing 100875, China
  • 收稿日期:2006-12-28 修回日期:2008-03-22 出版日期:2010-01-20 发布日期:2010-01-20
  • 基金资助:

    Supported partially by NSFC (10826052, 10671018).

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

  1. School of Mathematical Sciences (&|Laboratory of Mathematics and Complex Systems), Beijing Normal University, |Beijing 100875, China
  • Received:2006-12-28 Revised:2008-03-22 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    Supported partially by NSFC (10826052, 10671018).

摘要:

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 is that if k=1 for n=3 or 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).

关键词: fundamental groups, positive sectional curvature, group actions

Abstract:

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 is that if k=1 for n=3 or 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).

Key words: fundamental groups, positive sectional curvature, group actions

中图分类号: 

  • 53C20