Notes for Bott's 1963 lectures on Morse theory - MathOverflow

Notes for Bott's 1963 lectures on Morse theory

2012-12-06T15:23:49Z

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.

Answer by Dick Palais for Notes for Bott's 1963 lectures on Morse theory

2012-12-07T06:14:15Z

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.)

Answer by David Farris for Notes for Bott's 1963 lectures on Morse theory

2012-12-13T12:27:44Z

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.