Differential Topology - Differential Topology (Lecture II); Differential Topology (Lecture II)

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  • Credits (2011)
  • The following was videotaped August 30 to September 2, 1965 at Cornell University during the 46th Summer Meeting of the Mathematical Association of America, celebrating the association's 50th anniversary. The lectures were part of the Individual Lectures Project of the Committee on Educational Media of the Mathematical Association of America.
  • The Mathematical Association of America presents
  • Differential Topology (Lecture II)
  • with Professor John W. Milnor, Princeton University, Earle Raymond Hedrick Lectures 1965
  • Credits (1965)
  • An Individual Lectures Project, Committee on Educational Media, Mathematical Association of America Production
  • Differential Topology with Professor John W. Milnor, Princeton University
  • The Earle Raymond Hedrick Lectures, 1965, Lecture II
  • Defining terms: Concepts of manifolds in each of 3 categories already talked about
  • M is a topological manifold
  • Modify definition to apply to one of other categories: piecewise linear
  • Concept of a manifold with boundary
  • Concept of a manifold without boundary
  • Poincare Problem
  • How many distinct smooth manifolds of dimension n with the homotopy type of s n.
  • Analysis of problem Milnor presented.
  • Applies Smale's theorem.
  • Describes the manifold M in a new way.
  • Shows that manifold is isomorphic to the standard sphere using an elementary lemma.
  • Describes what relations there are between the categories.
  • Notion of C1 triangulation and what a triangulation is.
  • Whitehead proved several basic theorems.
  • Can put 4 categories in a definite order.
  • Concept of the Tangent Bundle.
  • Commutative diagram.
  • In reverse direction, one has the Inverse Function Theorem
  • Ends lecture.
  • End credits (1965)
  • An Individual Lectures Project, Committee on Educational Media, Mathematical Association of America Production
  • Produced for CEM by Professor A.N. Feldzamen, University of Wisconsin
  • Directed by Louis P. Levine
  • Financial support from the National Science Foundation; ©1965 Mathematical Association of America
  • Grateful appreciation is expressed to Professor Alex Rosenberg of the Mathematics Department, Cornell University and the Staff of the Statler Auditorium
  • Technical facilities by Tele-Tape Productions, New York City; Kinescopes by Reeves Studios
  • Recorded 1965 by videotape in the Statler Auditorium, Cornell University during the 50th Anniversary Meeting of the Mathematical Association of America
  • End credits (2011)
  • John Milnor was awarded the 2011 Abel Prize for pioneering discoveries in topology, geometry and algebra.
  • Digital re-mastering of this film in 2011 was a joint project of the Mathematical Sciences Research Institute and the Mathematical Association of America with generous support from the Simons Foundation.
  • Technical support and production: Monaco Labs, Zala Films
  • ©1965, 2011 Mathematical Association of America, All Rights Reserved