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Prof. Alexander F. Ritter Associate Professor, University of Oxford |
MORSE HOMOLOGY (Oxford graduate course, Michaelmas Term 2013) (Mondays and Thursdays 12-1 in C6, Mathematical Institute) LECTURE NOTES I would be extremely grateful for your feedback because these notes will be published as a book. Ideas, comments, corrections, anything. My contact details: find the contacts here My homepage: here HOMEWORKS (PDF): you have no obligation to do these, but it may help you understand the material to check these out. There are lots of hints so you don't end up spending too much time on them. Lecture 1 (PDF): A broad overview: Morse functions, topology of sublevel sets, Morse homology, number of critical points of a generic function, geometry vs functional analysis, Poincare duality via Morse homology I'm currently updating the notes from HERE, so please in the meantime look at those. This course will be quite similar to that one in the first few lectures, after which we may take a different route (the hope is to have a few lectures on Floer theory). ⋄ Also see the notes from the 2024 course on Morse Homology at Oxford: Morse Homology (TCC Graduate course) : Lecture notes here. |