This is the website of Fall 2017's Math 272x topics on diffeomorphisms of disks. Here is the course information:

  • The syllabus.
  • The details about the papers and topic suggestions can be found here.
  • All the lectures notes are collected in a book.

Lectures

Below appear the lecture notes and further references (thanks to Manuel Krannich, Sam Nariman and Jens Reinhold for comments and corrections).

  • 8/30, Lecture 1: Introduction.
  • 9/01, Lecture 2: The Whitney topology.
  • 9/04, Labor day.
  • 9/06, Lecture 3: Comparing diffeomorphism groups I: collars.
  • 9/08, Lecture 4: Comparing diffeomorphism groups II: the exponential map.
  • 9/11, Lecture 5: Comparing diffeomorphism groups III: convolution.
  • 9/13, Lecture 6: Smale's theorem.
  • 9/15, Lecture 7: Parametrized isotopy extension.
  • 9/18, Lecture 8: Embeddings of Rm.
  • 9/20, Lecture 9: Gramain's proof of Smale's theorem.
  • 9/22, Lecture 10: Hatcher's proof of the Smale conjecture.
  • 9/25, Lecture 11: Transversality I.
  • 9/27, Lecture 12: Transversality II.
  • 9/29, Lecture 13: Morse functions.
  • 10/2, Lecture 14: Handles.
  • 10/4, Lecture 15: Handle modification.
  • 10/6, Lecture 16: Handle exchange.
  • 10/9, Columbus day.
  • 10/11, Lecture 17: The s-cobordism theorem and the Poincare conjecture.
  • 10/13, Ben Knudsen's lecture: A Brieskorn sphere.
  • 10/16, Lecture 18: The Whitney trick.
  • 10/18, Lecture 19: Algebraic K-theory.
  • 10/20, Lecture 20: The theorems of Igusa and Waldhausen.
  • 10/23, Lecture 21: The Hatcher-Wagoner-Igusa sequence.
  • 10/25, Lecture 22: Isotopy classes of diffeomorphisms of disks.
  • 10/27, Lecture 23: The Hatcher spectral sequence and the Farrell-Hsiang theorem.
  • 10/30, Lecture 24: The Kirby-Siebenmann bundle theorem I.
  • 11/1, Lecture 25: The Kirby-Siebenmann bundle theorem II.
  • 11/3, Lecture 26: Flexibility and smoothing theory.
  • 11/6, Lecture 27: Homological stability for symmetric groups.
  • 11/8, Lecture 28: The Barratt-Quillen-Priddy-Segal theorem I.
  • 11/10, Lecture 29: The Barratt-Quillen-Priddy-Segal theorem II.
  • 11/13, Lecture 30: Homological stability for diffeomorphisms of Wg,1's I.
  • 11/15, Lecture 31: Homological stability for diffeomorphisms of Wg,1's II.
  • 11/17, Lecture 32: The homotopy type of the cobordism category.
  • 11/20, Lecture 33: Surgery in cobordism categories.
  • 11/22, Thanksgiving.
  • 11/24, Thanksgiving.
  • 11/27, Lecture 34: The Weiss fiber sequence.
  • 11/29, Lecture 35: Embedding calculus.
  • 12/01, Lecture 36: Finiteness results for diffeomorphisms of disks.

Math 272x Fall 2017