I am looking for resources (books, notes, lecture video, etc. anything will do although printed material in English is preferable) on foliations which satisfy some or all of the following constraints.
- Prerequisites: I am familiar with algebraic topology (in the geometric style, as in Hatcher), differential topology (as in Guillemin-Pollack), and Riemannian geometry (as in do Carmo) along with all other standard undergraduate topics (by which I mean content covered in standard textbooks in real and complex analysis, linear and basic algebra, commutative algebra, classical algebraic geometry, point set topology, curves and surfaces). I am also familiar with characteristic classes (Morita's differential forms book and Madsen-Tornehave), basic symplectic geometry (da Silva), and basic topological/measure theoretic dynamics (earlier chapters of Brin-Stuck).
I am also familiar with physics (general relativity using Caroll, classical mechanics using Goldstein, etc.) if it helps.
Ideally, I am looking for two types of resources. (Notice that the two are not mutually exclusive.)
An exposition of the theory which has a strong geometric taste (much like Hatcher's books) ideally with a lot of pictures and concrete examples. Ideally, the book connects new ideas introduced in the book with older ideas (described in "prerequisites" above).
Collection of problems which allows one to practice applying the theory. I prefer exercises which are not just filling in technical details which the author did not have time for. Instead, I prefer something which allows one to a.) learn key heuristics, and ideally b.) get a sense on why the theory will be important later in one's studies.
So far, I have the following books:
- Tamura, Topology of Foliations: An Introduction
- Calegari, Foliations and the Geometry of 3–Manifolds