Sources and component terms

Original lesson text, proofs, exercises and drawings are dedicated to the public domain under CC0 1.0. Human mathematical sources are credited alongside the arguments that use them. The following adaptation retains its source licence.

K-theory of the leaf space, Lemma 7.7 and its proof adapts the fibre-integrated module, tensor identification and mean-curvature connection of Jens Kaad and Walter D. van Suijlekom, Factorization of Dirac Operators on Almost-Regular Fibrations of Spin-c Manifolds, Documenta Mathematica 25 (2020), 2049–2084, Sections 2 and 3.1–3.2, especially Proposition 15 and Lemma 16. Copyright Deutsche Mathematiker-Vereinigung. The publisher identifies this exact article as CC BY 4.0: article and licence notice, published PDF, DOI.

This component and its expanded proof remain CC BY 4.0. Changes include notation, compact-base hypotheses, explicit coordinate and tensor arguments, and right Clifford coefficients in both parities. Reusers must retain the source attribution, this licence and an indication of their changes. No endorsement by the source authors is implied.

Editable course sources

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

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Companion readings

Read the companion lessons for the algebra, geometry, analysis and measure theory used in the course. Each reading identifies its mathematical sources and applicable component terms. The partition-of-unity reading gives a complete CC0 proof. The spectral theorem and its domain rules use CC0 readings, including Spectral products, transport and inverse domains. The additional reading Spectral measures with the original operator domain retained is licensed under GFDL 1.2.

Figures

Reader components

The reader uses the following open-source components, with their licence notices.

• Course renderer and adapter: CC0 1.0
• MathJax 3.2.2: Apache License 2.0
• markdown-it-py 3.0.0: MIT
• mdurl 0.1.2: MIT

Portable regeneration instructions · Build adapter