FIXED POINT FREE CIRCLE ACTIONS AND FINITENESS THEOREMS
FIXED POINT FREE CIRCLE ACTIONS AND FINITENESS THEOREMS
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DOI：
10.1142/s0219199700000062
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发表时间：
2000-02
影响因子：
1.6
通讯作者：
F. Fang;Xiaochun Rong
中科院分区：
文献类型：
--
作者：
F. Fang;Xiaochun Rong
We prove a vanishing theorem of certain cohomology classes for an 2n-manifold of finite fundamental group which admits a fixed point free circle action. In particular, it implies that any Tk-action on a compact symplectic manifold of finite fundamental group has a non-empty fixed point set. The vanishing theorem is used to prove two finiteness results in which no lower bound on volume is assumed. (i) The set of symplectic n-manifolds of finite fundamental groups with curvature, λ ≤ sec ≤ Λ, and diameter, diam; ≤ d, contains only finitely many diffeomorphism types depending only on n, λ, Λ and d. (ii) The set of simply connected n-manifolds (n ≤ 6) with λ ≤ sec ≤ Λ and diam ≤ d contains only finitely many diffeomorphism types depending only on n, λ, Λ and d.
