The aim of this minicourse is to present the classical theory of codimension 1 foliations. In the first session we shall explore the general methods in the theory of codimension 1 foliations: basic definitions, classification of minimal sets, Dippolito's decomposition of saturated open sets, Novikov's theorem, topology of the set of compact leaves and several examples and methods to construct codimension one foliations (suspensions, center-stable foliations, turbulization, transverse surgeries or open book decompositions). In the second session we shall deal with the classical results involving transverse regularity as the Sacksteder's and Denjoy's theorems, the theory of levels or the Haefliger's theorem on the non-existence of codimension one analytic foliations in certain manifolds.
It is assumed that the participants are familiar with the basics in geometry, topology, algebraic topology and dynamical systems.
Bibliography:
[1] A. Candel & L. Conlon. Foliations I, Graduate Studies in Math. 23, American Mathematical Society Providence, Rhode Island 1999.
[2] A. Candel & L. Conlon. Foliations II, Graduate Studies in Math. 60, American Mathematical Society Providence, Rhode Island 1999.
[3] C. Camacho & A. Lins Neto. Geometric theory of foliations. Birkhäuser, Boston-Basel-Stuttgart 1985.
© Carlos Meniño Cotón.