“Milnor's Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Milnor's Theorem

释义

Milnor's Theorem

If a Compact Manifold has Nonnegative Ricci Curvature, then its Fundamental Group has at mostPolynomial growth. On the other hand, if has Negative curvature, then its Fundamental Group hasexponential growth in the sense that grows exponentially, where is (essentially) the number ofdifferent ``words'' of length which can be made in the Fundamental Group.

References

Chavel, I. Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.

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