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.

• Fibonacci Hyperbolic Cosine
• Fibonacci Hyperbolic Cotangent
• Fibonacci Hyperbolic Sine
• Fibonacci Hyperbolic Tangent
• Fibonacci Identity
• Fibonacci Matrix
• Fibonacci n-Step Number
• Fibonacci Number
• Fibonacci Polynomial
• Fibonacci Pseudoprime
• Fibonacci Q-Matrix
• Fibonacci Sequence
• Fibration
• Field
• Field Axioms
• Field Extension
• Fields Medal
• Fifteen Theorem
• Figurate Number
• Figurate Number Triangle
• Figure Eight Knot
• Figure Eight Surface
• Figure-of-Eight Knot
• Figures
• Filon's Integration Formula