Companion readings

These lessons provide the algebra, topology, analysis and measure theory used in the foliation course. Each reading retains its own source credits and licence.

1. Nonunital algebras: unitization, relative classes and half-exactness · Markdown source
   CC0-1.0
2. Matrix stability, stability and continuity of \(K_0\) · Markdown source
   CC0-1.0
3. Invertibles, unitaries and \(K_1\) · Markdown source
   CC0-1.0
4. The index map and the exact sequence at \(K_0\) · Markdown source
   CC0-1.0
5. Suspension, higher K-groups and the long exact sequence · Markdown source
   CC0-1.0
6. Bott periodicity · Markdown source
   CC0-1.0
7. The six-term exact sequence and the exponential map · Markdown source
   CC0-1.0
8. Topological K-theory of spaces, pairs and vector bundles · Markdown source
   CC0-1.0
9. Idempotents, projections and their equivalences · Markdown source
   CC0-1.0
10. Vector bundles and finitely generated projective modules · Markdown source
    CC0-1.0
11. The Grothendieck group and \(K_0\) of a unital algebra · Markdown source
    CC0-1.0
12. Toeplitz operators and the index theorem on the circle · Markdown source
    CC0-1.0
13. Haar measure on locally compact groups · Markdown source
    CC0-1.0
14. Spectral measures with the original operator domain retained · Markdown source
    GFDL-1.2-only
15. Measured groupoids and transverse measures · Markdown source
    CC0-1.0
16. Square-integrable representations and random operators · Markdown source
    CC0-1.0
17. Weights on random operators and formal dimension · Markdown source
    CC0-1.0
18. The spatial derivative · Markdown source
    CC0-1.0
19. The Effros Borel structure · Markdown source
    CC0-1.0
20. Polish spaces and standard Borel spaces · Markdown source
    CC0-1.0
21. Manifold duality, the diagonal and Wu classes · Markdown source
    CC0-1.0
22. Vector bundles and their constructions · Markdown source
    CC0-1.0
23. Connections and parallel transport · Markdown source
    CC0-1.0
24. Local tools for bundles and transport · Markdown source
    CC0-1.0
25. AF-algebras · Markdown source
    CC0-1.0
26. C*-algebras: continuous functional calculus, automatic continuity, positive cones, approximate identities and quotients · Markdown source
    CC0-1.0
27. Groupoid C*-algebras: full and reduced · Markdown source
    CC0-1.0
28. Equivalence of groupoids and Morita equivalence of their C*-algebras · Markdown source
    CC0-1.0
29. The Rieffel correspondence and induced representations · Markdown source
    CC0-1.0
30. Imprimitivity bimodules and Morita equivalence · Markdown source
    CC0-1.0
31. Tensor products and C*-correspondences · Markdown source
    CC0-1.0
32. Cuntz algebras · Markdown source
    CC0-1.0
33. Cuntz–Krieger algebras, minimal systems and projectionless algebras · Markdown source
    CC0-1.0
34. Spectral products, transport and inverse domains · Markdown source
    CC0-1.0
35. Joint spectral cutoffs and graded tensor sums · Markdown source
    CC0-1.0
36. Finite conditional expectations, measurable densities, and positive kernel integrals · Markdown source
    CC0-1.0

Applicable component notices are linked from the readings that use them.