论文信息 - Topology from the differentiable viewpoint

Topology from the differentiable viewpoint

Preface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixed point theorem133Proof of Sard's theorem164The degree modulo 2 of a mapping20Smooth homotopy and smooth isotopy205Oriented manifolds26The Brouwer degree276Vector fields and the Euler number327Framed cobordism the Pontryagin construction42The Hopf theorem508Exercises52AppClassifying 1-manifolds55Bibliography59Index63

J. Milnor

[1] B. Kerékjártó,et al. Vorlesungen über Topologie: I, Flächentopologie , 1923 .

[2] H. Hopf,et al. Abbildungsklassenn-dimensionaler Mannigfaltigkeiten , 1927 .

[3] H. Hopf. Über die Abbildungen von Sphären auf Sphäre niedrigerer Dimension , 1935 .

[4] H. Whitney. A Function Not Constant on a Connected Set of Critical Points , 1935 .

[5] A. Morse,et al. The Behavior of a Function on Its Critical Set , 1939 .

[6] On Total Curvatures of Riemannian Manifolds: I , 1940 .

[7] S. Chern. A simple instrinsic proof of the Gauss Bonnet formula for closed Riemannian manifolds , 1944 .

[8] N. Steenrod. Topology of Fibre Bundles , 1951 .

[9] J. Milnor. On Manifolds Homeomorphic to the 7-Sphere , 1956 .

[10] S. Smale. Generalized Poincare's Conjecture in Dimensions Greater Than Four , 1961 .

[11] C. Wall. Classi?cation of (n ? 1)-connected 2n-manifolds , 1962 .

[12] M. Hirsch. A proof of the nonretractibility of a cell onto its boundary , 1963 .

[13] S. Smale. A survey of some recent developments in differential topology , 1963 .

[14] S. Sternberg. Lectures on Differential Geometry , 1964 .

[15] S. Lang. Introduction to Differentiable Manifolds , 1964 .

[16] J. Munkres,et al. Calculus on Manifolds , 1965 .