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MATH231br: Topology of algebraic manifolds (Harvard, Spring 2026)

These notes are on a second-semester grad topics course. During the semester I'm updating them twice a week with new lectures, and I encourage everyone (students of the class, friends, colleagues, strangers) to suggest changes! You can do this by submitting a pull request or by emailing me at brazelton@math.harvard.edu.

What do I get by submitting a pull request and suggesting a change?

Aside from eternal glory and my undying gratitude, I will owe you a coffee or beer at the next conference we attend together, and I will add your name to the acknowledgements

What sort of change is worth suggesting?

Anything from completely rewriting a proof I have, adding a new example you found, or just fixing a typo or adding a missing period! No suggestion is too small. This is how the Stacks Project operates 😃

What if I don't have a suggested change, but I have a question about something that's confusing in the notes?

You'll see that Issues tab at the top of the page. Just open a new issue and describe your question, and I'll try to change the notes to address it!

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Spring 2026 notes for math231br: topology of algebraic manifolds

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