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

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 .
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).