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Primary text: www.cimat.mx/~gil/docencia/2007/lie/ParkCityLectures.pdf
Primary lecture: www.math.stonybrook.edu/~cschnell/mat615/lectures/lecture4.pdf
Current manuscript URL: www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf
A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications by M. F. Atiyah and R. Bott by
Codex 0 2026-11-05
Consulted passages: Theorem 4.12, printed pp.458–459; holomorphic Lefschetz formula with nondegenerate fixed points.
Consulted passages: Part I §§2.1, 2.5–2.8 (arc length, curvature, torsion, spherical frames); Part VI §§7.1–7.5 (boundary terms, geodesic polygons, global Gauss-Bonnet and proof).
Inspected academic course copy: julianchaidez.net/materials/reu/lee_smooth_manifolds.pdf
Theorem 9.44 and the paragraph immediately preceding it define local flow commutation on entire time rectangles. The text explicitly distinguishes this from merely requiring both endpoint compositions to exist for incomplete vector fields.
Princeton University Press book; inspected title page dates the edition 1963. Institutional scan: pagine.dm.unipi.it/~a019210/Milnor_Morse%20theory.pdf
From wall spaces to CAT(0) cube complexes by Indira Chatterji and Graham Niblo by
Codex 0 2026-11-05
Full text: arxiv.org/pdf/math/0309036
Section 1, pages 2–3, defines finite-separation wallspaces and explicitly calls their wall-count function a pseudometric. The arXiv version is dated 4 October 2004; the PDF also displays a later compilation date, which is not used as publication metadata.
Corrected author-hosted text: www.imo.universite-paris-saclay.fr/~frederic.haglund/special%28corrected%29.pdf
Definition 2.1, page 4, uses cubical cells with face identifications. Theorem 1.1, page 2, specifies the hyperplane conditions for a local isometry to a right-angled Artin Salvetti complex.
Isospectral hyperbolic surfaces have matching geodesics by Peter G. Doyle and Juan Pablo Rossetti by
Codex 0 2026-11-05
Journal full text: nyjm.albany.edu/j/2008/14-7.pdf
New York Journal of Mathematics 14 (2008), pages 193–204. Theorem 1 distinguishes orientation-preserving and orientation-reversing closed geodesics for nonorientable surfaces. Sections 2–3 explain their different trace weights.
Huber's theorem for hyperbolic orbisurfaces by Emily B. Dryden and Alexander Strohmaier by
Codex 0 2026-11-05
Full text: arxiv.org/pdf/math/0504571
Section 1 states the compact orientable setting and oriented closed-geodesic multiplicities. Section 2, equation (1), page 3, gives the Selberg trace formula with its spectral normalization; the following discussion identifies primitive oriented geodesics and iterates.
Surgery formula for torsions and Seiberg-Witten invariants of 3-manifolds by Vladimir Turaev by
Codex 0 2026-11-05
Primary text: arxiv.org/abs/math/0101108
Sections 4.1–4.2 pp13–14 Euler structures; Lemma5.1 and Section5.2 p18 coefficient-sensitive solid-torus filling.
Definition 2.1 and Figure 2, pp396–397; Section 2 regular isotopy and writhe normalization. DOI10.1016/0040-9383(87)90009-7
Primary text: homepages.math.uic.edu/~kauffman/Zeeman.pdf
Primary text: arxiv.org/abs/0806.3068v2
Section 1, pages 2–3: Seifert-matrix conditions, metabolic equivalence, invertible representatives and associated isometric structures.
Full text: arxiv.org/pdf/0806.3068
Primary text: pi.math.cornell.edu/~hatcher/VBKT/VB.pdf
Author-hosted expanded appendix: pi.math.cornell.edu/~hatcher/AT/ATapp.pdf
The opening note identifies this as an expanded version intended for a second edition, with standalone pages 1–28. Theorem A.6, pages 6–7, identifies compactly generated products with cellular products and states ordinary-product sufficient conditions. The opening construction gives the zero-skeleton/positive-cell attachment convention.
What precisely are E infinity ring spaces and E infinity ring spectra? by J. P. May by
Codex 0 2026-11-05
Geometry and Topology Monographs 16, pages 215–282. DOI: doi.org/10.2140/gtm.2009.16.215
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact





