We consider nonnegatively curved 4-manifolds that admit effective isometric actions by finite groups and from that draw topological conclusions about the manifold. Our first theorem shows that if the manifolds admits an isometric Z_p x Z_p for p large enough that the manifold has Euler characteristic less than or equal to five. Our second theorem requires no hypothesis on the structure of the group other then that it be large but it does require the manifold to be δ —pinched, in which case we can then again conclude that the Euler characteristic is less than or equal to five.
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机译：我们考虑非负弯曲的4流形，它允许有限组进行有效的等距作用，并从中得出关于流形的拓扑结论。我们的第一个定理表明，如果流形对于p的等距Z_p x Z_p足够大，以使流形具有小于或等于5的欧拉特性。我们的第二个定理不需要假设该群的结构就大，但是它确实需要将流形压缩δ，在这种情况下，我们可以再次得出欧拉特征小于或等于5的结论。
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