## Yu.Burman

## Geometry of the spaces of mappings

### Course synopsis

- Mapping class group of a 2-torus.
- Thom's transversality theorem
- Whitney's fine topology
- Massive sets and Baehr principle
- Transversality and Sard's lemma
- Proof
- Typical self-intersections
- Smale--Hirsch principle
- Immersions of spheres and Smale paradox

- Frobenius theorem
- Proof
- Foliations: Reeb foliation and other examples
- Symplectic leaves
- Almost complex structures: Frobenius criterion.
- Almost complex structures tamed by a symplectic structure.

- Functions without critical points.