Characteristic classes: licensing and provenance
The independently written lessons, proofs, examples and solved exercises in this course are dedicated to the public domain under CC0 1.0.
The writing AI is GPT-6.1 Sol (OpenAI), running at Ultra. Claude Opus 5.5 (Anthropic) wrote the rotation-group starting example in Projective tangent bundles and their obstructions, the circle-bundle calibration in Chern classes and the integral universal ring and the proof of Lemma 8.1 in Grassmannians and classifying maps. Published lessons state their own author-instance AI self-check status. No independent AI or human review is claimed without a separately identified record.
Mathematical reading sources are freely accessible author texts, papers and lecture notes. The course supplies a proof of every result it uses, either in the lesson or in an earlier linked programme lesson. Source citations are additional reading, not substitutes for proofs. Referenced works retain their own rights.
Hatcher's author-hosted Spectral Sequences, Chapter 1, is also a scholarly reference. The homotopy and spectral-sequence companion supplies independently written proofs and solved exercises. The rational-homotopy companion supplies a complete filtered-chain proof of the higher-page multiplicative identity left open in that scholarly draft, and independently written proofs of the rational one-group calculation and sphere finiteness.
The rational-bordism conclusion independently proves explicit finite-stage bounds, the oriented rank theorem, projective polynomial generators and positive-multiple bounding criterion. Its source notes link the freely readable treatments by René Thom, Haynes Miller and Daniel Freed.
The signature chapter supplies independently written form algebra, relative boundary duality, the complete product proof, universal multiplicative-sequence construction, formal residue calculation and signature theorem, with original solved exercises. Further reading is Friedrich Hirzebruch's freely readable 1953 article and John Milnor's 1957 lecture notes, with notes by James Stasheff. The section includes the two-example signature calibration and balanced sphere-product calculation written by the AI.
The higher-diagonal mathematical formula is attributed to Anibal M. Medina-Mardones, arXiv:2105.08025v3. Its arXiv distribution licence does not permit republication of protected text. The course's cancellation argument, Cartan proof, teaching and exercises are independently authored; no paper text or algorithm is reproduced.
The website's renderer, MathJax and fonts retain the notices provided by Open Mathematics Courses.
The odd-prime companion independently supplies normalized-chain and cyclic-resolution algebra, higher diagonals, reduced-power properties and the Thom/polynomial/Wu proof, with six original solved exercises. Its references include J. Peter May's author-hosted paper and the freely readable 1957 lecture notes. Their protected text, files and exercise sets are not republished.
The triangulation companion independently supplies quantitative embedding stability, relative boundary extension, compact PL comparison and the coned eight-dimensional integral-refinement obstruction, with six original solved exercises. Its references link freely readable papers by John Milnor and official lecture notes by Jacob Lurie.
The unoriented bordism companion independently supplies the complete mod-two one-group calculation, square basis, finite comparison and free Thom-module detection proof, with six original solved exercises. Miller and Hatcher are scholarly sources.