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.

• Curlicue Fractal
• Curl Theorem
• Current
• Curtate Cycloid
• Curtate Cycloid Evolute
• Curvature
• Curvature Center
• Curvature Scalar
• Curvature Vector
• Curve
• Curve of Constant Breadth
• Curve of Constant Precession
• Curve of Constant Slope
• Curve of Constant Width
• Curvilinear Coordinates
• Cushion
• Cusp
• Cusp Catastrophe
• Cusp Form
• Cusp Map
• Cusp Point
• Cutting
• Cut-Vertex
• CW-Approximation Theorem
• CW-Complex