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 III)
with Professor John W. Milnor, Princeton University, Earle Raymond Hedrick Lectures 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 III
Beginning of Milnor lecture
To each plane of dimension n through the origin
Important use of the Grassman manifold: generalized Gauss map associated with a manifold
Illustrates the construction with a problem
Look at homology theory
Fundamental class of the manifold
Fundamental theorem of oriented cobordism theory
Notion of tangent bundle and notion of a vector bundle
Tangent bundle of a smooth manifold
2 examples of vector bundles (Grassman and tangent) related by the Gauss mapping
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
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