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Differential Topology (Lecture II)

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Table of Contents 
  •  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. 
 
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Metadata

Title:Differential Topology (Lecture II)
Identifier:e_math_01201
Description:The second 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:2R768C-D
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)
Reeves Studios (kinescope)
Language:en
PublisherDolph Briscoe Center for American History
Original Format:Film negative, 16mm