Additional and planned readings

Planned bivariant prerequisites

The bivariant conclusions that invoke the following programme lessons remain conditional on their stated proof prerequisites. This collection does not supply those planned proofs.

• Kasparov products: planned proof prerequisite.
• Thom isomorphisms and K-orientations in KK: planned proof prerequisite.
• Asymptotic morphisms and E-theory: planned proof prerequisite.
• Wrong-way maps for K-oriented maps: planned proof prerequisite.

Additional readings

The following lessons occur in later examples, comparison notes or further reading of the supporting texts. They are outside the exact proof sections imported by KT-CP and are not included in this supporting collection.

• Cauchy data from jumps and residues (AN-03).

• Causal kernels, initial data, and short-time geometry (AN-03).

• Changing an interior frame to extend an invertible matrix (AN-03).

• Solving an elliptic system from compatible boundary measurements (AN-03).

• Inductive limits and the K-theory of AF and AT algebras (KT-OPK).

• Hilbert modules and fields on the leaf space (NCG-FOLIATIONS).

• K-theory of the leaf space (NCG-FOLIATIONS).

• Transverse measures of foliations (NCG-FOLIATIONS).

• Tensor positivity and nuclearity (OA-APPROX).

• Atomic representations and measurable lifts (OA-FOUND-REMAINDER).

• Monotone approximation and semicontinuous operators (OA-FOUND-REMAINDER).

• Multipliers and essential extensions (OA-FOUND-REMAINDER).

• Analytic elements and strip arguments (analytic-elements-strips-and-kms).

• Completely positive maps (foundations-of-von-neumann-algebras).

• Integral representations of states (foundations-of-von-neumann-algebras).

• Projections and types of von Neumann algebras (foundations-of-von-neumann-algebras).

• The spectral theorem for bounded self-adjoint operators (foundations-of-von-neumann-algebras).

• The universal enveloping von Neumann algebra of a \(C^*\)-algebra, and \(W^*\)-algebras (foundations-of-von-neumann-algebras).

• Weak topologies: Tychonoff, Banach–Alaoglu, Mazur, bipolars, Krein–Milman and Eberlein–Šmulian (foundations-of-von-neumann-algebras).

• Square-integrable representations and random operators (noncommutative-integration).

• Traces on von Neumann algebras (traces-and-noncommutative-integration).

• Lebesgue’s covering theorem and the dimension of cubes (index-theory-of-elliptic-operators): further reading on the reverse dimension inequality.