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Differential Topology (Lecture III)

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Table of Contents 
  •  Beginning of Milnor lecture 
  •  Grassman manifold 
  •  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 
  •  Grassman bundle 
  •  2 examples of vector bundles (Grassman and tangent) related by the Gauss mapping 
  •  G exists and is unique up to homotopy 
  •  Examines 3 categories simultaneously: differentiable, piecewise linear, topological 
  •  For each x in our manifold, there exists a neighborhood use of x 
  •  Impose restriction that these neighborhoods' use of x will vary nicely with x 
  •  Impose condition of local triviality 
  •  Notion of tangent bundle in any one of the 3 categories 
  •  End of lecture 
 
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Metadata

Title:Differential Topology (Lecture III)
Identifier:e_math_01202
Description:The third in a series of three lectures given by John W. Milnor to the 46th Summer Meeting of the Mathematical Association of America. Black and white picture with sound.
Country:United States
State:New York
City:Ithaca
Date:1965/08/30-1965/09/02
CreatorMilnor, John W. (lecturer)
Location:2R768E-F
Source:Mathematical Association of America Records
Contributor:Wilder, Raymond Louis (introduction)
Levine, Louis P. (director)
Mathematical Association of America
The National Science Foundation (financial support)
Tele-Tape (technical facilities)
Language:en
PublisherDolph Briscoe Center for American History
Original Format:Film negative, 16mm