Topology from the differentiable viewpoint

  title={Topology from the differentiable viewpoint},
  author={John W. Milnor},
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… 
This paper develops the theory of differential topology, the study of manifolds and smooth maps between manifolds, towards investigating the classification of homotopy classes of smooth maps to the
On the homotopy classification of proper Fredholm maps into a Hilbert space
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We give the original proof of Rochlin’s famous theorem on signatures of smooth spin 4-manifolds, which uses techniques from algebraic topology. We have attempted to include enough background and
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A survey of some recent developments in differential topology
1. We consider differential topology to be the study of differentiable manifolds and differentiable maps. Then, naturally, manifolds are considered equivalent if they are diffeomorphic, i.e., there
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SHORTER NOTES The purpose of this department is to publish very short papers of an unusually elegant and polished character, for which there is nor- mally no other outlet. A PROOF OF THE
The Behavior of a Function on Its Critical Set
Referring to the next section for any unfamiliar notation or definition, let us consider the following statement. If m > 0 n > 1, R is an open subset of En , and f is a function on R to El of class
Über die Abbildungen von Sphären auf Sphäre niedrigerer Dimension
Die Frage, fur welche Dimensionszahlen N und n mit N>n es moglich ist, die Sphare S N wesentlich auf die Sphare S n abzubilden1), ist meines Wissens bisher nur in zwei Fallen beantwortet: 1. Fur
dc, Varieles differentiables
  • Paris : Hermann,
  • 1955