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 R*.^{m} - 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 W*._{g,1}'s I - 11/15, Lecture 31:
*Homological stability for diffeomorphisms of W*._{g,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*.