Math 516: The h-principle in topology.

The topic for this course is Gromov's h-principle and its applications in topology. The h-principle is a far-reaching tool arising from the example of Smale-Hirsch immersion theory, with applications to such seemingly disparate topics as foliations, cobordism theory, Riemannian geometry, and symplectic topology.


Course syllabus.
Lectures 1 and 2: Overview.
Lecture 3: Immersion theory. Notes by Owen Gwilliam. Last edited on 1/17/11.
Lecture 4: Flexible sheaves. Last edited on 1/26/11.
Lectures 5 & 6: The Hirsch-Smale theorem. Notes by Chris Elliott. Last edited on 1/25/11.
Lecture 7: Fibrations in immersion theory, part 1. Notes by Irina Bobkova. Not yet edited.
Lecture 8: Fibrations in immersion theory, part 2. Notes by Ian Le coming soon.
Lecture 9: Immersions into Euclidean spaces, from Smale to Cohen. Notes by Marc Hoyois. Last edited on 1/31/11.
Lecture 10: Eversing the 2-sphere. Notes by Agnès Beaudry.
Lecture 11: The h-principle for differential relations. Last edited on 2/7/11.
Lecture 12: Foliations and Haefliger structures. Notes by Owen Gwilliam. Last edited on 2/12/11.
Lecture 13: Classifying foliations. Notes by Takuo Matsuoka. Last edited on 2/14/11.
Lecture 14: Haefliger's theorem classifying foliations on open manifolds. Notes by Marc Hoyois. Last edited on 2/19/11.
Lecture 15: Overview of results on the classifying spaces for foliations. See Hurder's survey.
Lecture 16: Configuration spaces with annihilation and with labels. Last edited on 2/19/11.
Lecture 17: The sheaf of configuration spaces and the scanning map. Last edited on 2/22/11.
Lecture 18: The proof of McDuff's theorem, first part. Notes by Chris Elliot. Last edited on 2/24/11.
Lecture 19: The proof of McDuff's theorem, second part. Notes by Owen Gwilliam. Not yet edited.
Lecture 20: The h-principle for microflexible sheaves. Notes by Agnès Beaudry. Not yet edited.
Lecture 22: The Goodwillie-Weiss calculus of presheaves on manifolds. Notes by Takuo Matsuoka. Not yet edited.
Lecture 23: Polynomial approximation in Goodwillie-Weiss calculus. Notes by Irina Bobkova. Not yet edited.