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Would anybody happen to know where I could obtain a scanned version of

Lectures on Morse theory - [revised and expanded version of notes of lectures delivered at Professor R. Bott's topology seminar at Harvard in February and March of 1963], taken by Richard S Palais?

As far as I am aware, these notes were never published.

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    $\begingroup$ Note that Dick Palais participates in MO and has his email address posted at UC Irvine. It's worth consulting him. Also, Bott was very fond of Morse theory and lectured many times on the subject. It's worth checking his collected papers published by AMS. One survey (available online at www.ams.org/journals/): Lectures on Morse theory, old and new. Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 331–358. $\endgroup$
    – Jim Humphreys
    Commented Dec 6, 2012 at 16:54
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    $\begingroup$ P.S. The four volumes of collected papers were actually published by Birkhauser Boston (not AMS), but probably don't include those unpublished lectures. $\endgroup$
    – Jim Humphreys
    Commented Dec 6, 2012 at 20:40
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    $\begingroup$ These notes were published by Benjamin in 1969 under the title "Lectures on K(X). Here is a link to a scanned copy: google.com/… $\endgroup$
    – Carl Futia
    Commented Dec 6, 2012 at 20:58
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    $\begingroup$ P.S. Just noticed that this is a scan of an autographed copy. Can't do better than that! $\endgroup$
    – Carl Futia
    Commented Dec 6, 2012 at 21:03
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    $\begingroup$ Carl, I don't think these are the same notes. Bott also has notes giving an exposition of Morse theory, which is what I am after. $\endgroup$
    – user332
    Commented Dec 7, 2012 at 1:05

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I find myself more than a little confused by this question. First, the "Lectures on K(X)" are not about Morse Theory. It is true that I gave a lecture on Morse Theory at Bott's Seminar in 1963, but I did not take and write up notes of lectures by Bott (at least not as far as I can recall---but that was half a century ago). The lecture I gave was on extending Morse Theory to Hilbert manifolds using "Condition C" (later called Condition PS). At the end of that lecture someone in the audience told me he had heard a similar lecture by Steve Smale at Columbia a few weeks earlier. (By a weird coincidence, Steve had also called (essentially) the same condition Condition C.) Anyway, I contacted Steve and we wrote up a joint research announcement in BAMS (called "A Generalized Morse Theory") and I wrote up my full version (called "Morse Theory on Hilbert Manifolds") in Topology and Steve wrote up his full version in the Annals. (The reason we didn't write a joint article was that we had pretty much already completed our research and although we had essentially the same abstract theory we had each developed it for very different applications.)

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    $\begingroup$ I did some more searching with Google and found that Amazon has a reference to: "Lectures on Morse theory: [revised and expanded version of notes of lectures delivered at Professor R. Bott's topology seminar at Harvard in February and March of 1963 [Unknown Binding] Richard S Palais (Author)" with Brandeis Univ, listed as the publisher. I suspect this must have been an early preprint version of "Morse Theory on Hilbert Manifolds" $\endgroup$
    – Dick Palais
    Commented Dec 7, 2012 at 6:31
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    $\begingroup$ Dick, many thanks for positing the history of "Palais-Smale"! $\endgroup$
    – Deane Yang
    Commented Dec 7, 2012 at 12:02
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There actually is a Morse theory book by Bott, but it's not the one you cite. Rather, it's the 1960 volume Morse theory and its application to homotopy theory with the attribution "Lectures by R. Bott / Notes by A. van de Ven". It's a little red book, but my copy (given to me by Bott himself!) is in a box in the rafters of my parents' garage at the moment, so I can't say anything else about it. Content-wise, it's similar to Milnor's Morse Theory, but a bit more terse.

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  • $\begingroup$ do you still have this copy? (I am interested in it, if we can talk via email) $\endgroup$
    – Chris Gerig
    Commented Sep 24, 2013 at 3:06

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