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I plan to write my maths masters' dissertation on discrete Morse theory. I intend to write it from a theoretical point of view, relating it to classical Morse theory. I still have to decide exactly what to do, but I would like to learn the basics about discrete Morse theory first.

Which books or articles would you recommend to introduce myself to the topic? I wonder if "A user's guide to discrete Morse theory" by R. Forman or "Discrete Morse Theory" by N. Scoville are good starting points.

Thanks!

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  • $\begingroup$ I learned the basics from the applied setting here arxiv.org/abs/2003.03844. May be useful. It can get very theoretical but the idea is simple, so maybe don't read a whole book to start off as that can take many months. $\endgroup$
    – apg
    Jan 7, 2022 at 15:52

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Try A User's Guide to Discrete Morse Theory by Robin Forman, who is a top expert. Its 44 pages so not too long for a master's thesis. Also don't forget the usefulness of recorded seminars and youtube videos, as this subject is quite new in its applications.

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  • $\begingroup$ Thank you! Do you have any particular seminars/videos in mind that you would recommend? $\endgroup$
    – MathMole
    Jan 7, 2022 at 16:29
  • $\begingroup$ Vidit Nanda here for example youtube.com/watch?v=QD4-qm2-vTA $\endgroup$
    – apg
    Jan 10, 2022 at 14:44

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