Hypotheses and scope of the transverse normal constructions.

Foliations and their operator algebras

Transverse measures and currents, holonomy C*-algebras, Hilbert modules, measured Euler and index formulas, and the K-theory of a leaf space.

Five lessons in English, with examples, exercises, solutions and 162 diagrams. Read the lessons in this order:

1. Transverse measures of foliations · Markdown
2. The C*-algebra of a foliation · Markdown
3. Hilbert modules and fields on the leaf space · Markdown
4. The index theorem for measured foliations · Markdown
5. K-theory of the leaf space · Markdown

Proved scope and remaining questions · Sources, figures and component terms · Companion readings · Download reader and editable sources