I keep running across papers that refer to a set of lecture notes by Robert MacPherson at MIT during the fall of 1993 on Perverse Sheaves. There might also be a set of notes from lectures in Utrecht in 1994 taken by Goresky. For references to these elusive, unpublished notes see the work of Maxim Vybornov and A. Polishchuk.

Does anyone have a copy or know how I could obtain a copy?


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    $\begingroup$ here faculty.tcu.edu/gfriedman/notes are notes on intersection homology and perverse sheaves by Robert MacPherson. But they are from 1990, so you are propably looking for something else (?). $\endgroup$ Apr 26, 2010 at 17:53
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    $\begingroup$ Local MacPherson students Braden and Gunnells tell me they took notes of their own (incomplete), but suggest that Vybornov's thesis would be a better source anyway if that's findable. $\endgroup$ Apr 26, 2010 at 18:11
  • $\begingroup$ @Jonas This is a great set of notes! I think you should make it an answer. For anyone else, is it possible these were the same notes MacPherson used at MIT? $\endgroup$ Apr 26, 2010 at 19:19

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The notes on Friedman's page are great -- they were very helpful when I was learning about perverse sheaves as a graduate student, since they explain how to think about middle perversity perverse sheaves on complex analytic spaces with complex stratifications (the case of most interest for most people) without having to first define the derived category. Unfortunately the main result there, although it is a theorem, is not fully proved in the notes. One of Bob's students, Mikhail Grinberg, had a project to fill in the details and flesh out the notes into a book, but he left mathematics for a job at Renaissance Technologies. He taught a course at MIT around 2000 where he went through the steps needed to fill in the proof. Perhaps someone has usable notes from that class?

The 1993 course was quite different. Again the goal was to see perverse sheaves and their abelian category structure without going through the derived category, but he was working with arbitrary perversities on a regular cell complex. By putting weird "phantom dimensions" on the cells and putting arrows between cells of adjacent phantom dimensions you get a quiver whose representations are perverse sheaves constructible for the cell complex structure. But it's hard to use this to compute beyond simple examples, because the cell complexes would have to be very large, and it's hard to define the condition that gives constructibility for a coarser stratification like a complex analytic one.

  • $\begingroup$ Thanks for the clarification and context of the notes! The quiver take on things might be relevant for my research. Do you have a nice reference? Thanks again. $\endgroup$ Apr 27, 2010 at 13:36
  • $\begingroup$ Besides the papers of Vybornov and Polishchuk, which you've already seen, I don't know another place where those ideas have appeared. $\endgroup$
    – Tom Braden
    May 6, 2010 at 17:24

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