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Lectures on the h-Cobordism Theorem

John Milnor

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Geometrie

Beschreibung

Important lectures on differential topology by acclaimed mathematician John Milnor

These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.

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Schlagwörter

Differential equation, Bounded set (topological vector space), Variable (mathematics), Cohomology, Diffeomorphism, Hyperbolic function, Topology, Existence theorem, Contractible space, Partial derivative, Intersection (set theory), Implicit function theorem, Sphere theorem (3-manifolds), Smoothness, Scalar multiplication, Integral curve, Characterization (mathematics), Intersection number (graph theory), Simply connected space, Support (mathematics), Partition of unity, Differentiable manifold, Critical point (mathematics), Function (mathematics), Topological space, Uniqueness theorem, Inverse function theorem, Vector field, Embedding, Hessian matrix, Universal coefficient theorem, Ambient isotopy, Commutative diagram, Neighbourhood (mathematics), Inclusion map, Exponential map (Riemannian geometry), Isomorphism theorem, Manifold, Degeneracy (mathematics), Disk (mathematics), Tangent space, Ordinary differential equation, Fundamental group, Elementary proof, H-cobordism, Continuous function, Theorem, Homotopy, Infimum and supremum, Tangent bundle, Morse theory, Polynomial, Parity (mathematics), Intersection number, Diagram (category theory), Cobordism, Existential quantification, Projection (mathematics), Submanifold, Symmetric space, Codimension, Exponential map (Lie theory), Corollary, Basis (linear algebra), Equivalence class, Identity matrix, Stiefel manifold, Generalized Poincaré conjecture, Transitive relation, Equivalence relation