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.