# Sergei Yakovenko's blog: on Math and Teaching

## Wednesday, November 7, 2007

### “Auxiliary Lesson” שעור עזר) #3) November 8, 2007

Filed under: lecture — Sergei Yakovenko @ 3:28
Tags: , ,

Holomorphic singular foliations

1. Definition of foliation. Different types of equivalence of foliations.
2. Equivalence of foliations vs. equivalence of vector fields. Foliations as “phase portraits” of holomorphic vector fields.
3. Examples of foliations: Cartesian products, bundles, constant flow on the torus.
4. Holonomy of foliations: construction, invariance.
5. Singular foliations. Singular locus, its structure. Singular loci of planar foliations. Germs of singular foliations.
6. Digression: local structure of complex analytic subsets of $(\mathbb C^2,0)$.
7. Complex separatrices and their holonomy.
8. Example: holonomy of foliations generated by linear vector fields.
9. Suspension: realization of a given holonomy by a foliation.

Preliminary reading before the meeting: Textbook section 2 (printing disabled) andFirst Aid (sections A6-A8).

1. A request: Sergei, could you post the book’s updated reference list, since there were few changes from the published draft?

Comment by Roy Malka — Saturday, November 10, 2007 @ 10:45

2. Roy: here it goes: Bibliography.

Comment by Sergei Yakovenko — Sunday, November 11, 2007 @ 9:36

3. It is too bad there was no time for the digression on local structure of analytic sets…

Comment by Gal Binyamini — Monday, November 12, 2007 @ 11:29

4. Gal: I am afraid that I would be able only to formulate the results in any case. Look for the first aid.

Comment by Sergei Yakovenko — Tuesday, November 13, 2007 @ 6:17

Blog at WordPress.com.