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I am an active part of a research project on the positive effects of open math projects on the community. With open math projects I have in mind a particular thing, namely a GIT project on mathematics in which everyone can contribute and the final result is a collaborative text about some part of mathematics. The obvious examples are The stacks project, The HoTT book, Open logic project. I would like to know other examples of this kind of project. I am specially interested in those projects that have already finished (succeeded).

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Here are six fairly specific examples that I know of; in each case, the writers have welcomed collaboration.

  1. Eric Peterson's formal geometry notes, on using bordism operations and some formal algebraic geometry in homotopy theory. Though the class is complete, the notes are still in progress.
  2. Eric Peterson's vector fields on spheres notes, from a class taught by Haynes Miller. These notes are still in progress.
  3. Sanath Devalapurkar's notes from two algebraic topology classes taught by Haynes Miller.
  4. Andy Neitzke's notes on applications of quantum field theory to geometry, for a class currently being taught at UT Austin (so the notes are still in progress).
  5. Andy Neitzke's notes on the moduli space of Higgs bundles, from a class taught a few years ago.
  6. My notes on equivariant homotopy theory, from a class taught by Andrew Blumberg. The notes are stable, but not completed.
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There's some repos I know:

I tried this a few times myself:

  • Infinite-dimensional Lie algebras (notes from a class by Pavel Etingof). These notes cover something like 1/2 of the class (all that I have fully understood). Arguably a lot of things could be improved (the subject is typically done with an amount of handwaving unusual for algebra, and I had to introduce some formalism to make things rigorous; this formalism is often awkward). I really wouldn't mind if someone came along and continued the job ;)

  • Notes on the combinatorial fundamentals of algebra. The basics of combinatorics (permutations, signs, etc.) necessary to build up determinants, and some determinantal identities, written up in high detail and with numerous exercises. (The length is due to the detailed proofs; the content itself covers perhaps half of a semester of discrete maths and algebraic combinatorics.)

  • I tried writing notes for a linear algebra class and for a graph theory class. Result is I got the first 4-5 (resp. 2-3) lectures written up, then dropped it, as I ran out of time. Probably needs more iterations (or a 1/0 teaching load...).

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    $\begingroup$ The current CRing project seems to be now maintained by Markus J. Pflaum, who also has another open book project FANCy on Functional Analysis and Noncommutative Geometry. Both have git repositories. $\endgroup$ – Igor Khavkine Oct 3 '17 at 7:26

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