Foliations

Prof. Gianluca Bande
Dipartimento di Matematica e Informatica
Università degli Studi di Cagliari

Abstract

The course is an introduction to the Theory of Foliations. Basic knowledge of Differential Geometry is required and the basics of Fundamental Group.

Outline

– Definition(s) and examples of Foliations. Dynamical systems. Frobenius’ Theorem.
– Holonomy of a leaf and the Reeb Stability Theorem. Basic and foliated Cohomology. Godbillion-Vey class for a codimension 1 foliation on a 3-manifold.
– The Reeb foliation: definition and a 3D-printer model. Novikov and Likorisch Theorem.

Schedule

The course spans over 3 lectures of 2 hours each (6 hours total). The lectures will be given on February 5, February 12, February 15 – 2024 at 4:30 p.m. in Room B of the Department of Mathematics and Computer Science.

Exam

The final exam consists in a presentation.

References

1. C. Camacho and A. Lins Neto, Geometric theory of foliations, Birkhäuser, 1985.
2. A. Candel; L. Conlon, Foliations I, Grad. Stud. Math. 23, American Mathematical Society, Providence, 2000.
3. P. Tondeur, Geometry of Foliations, Monogr. Math 90, Birkhäuser Verlag, Basel, 1997.