[Math] What are good Morse Theory lecture notes and books

Question

Searching on the net I couldnt find any recent lecture/course notes on Morse Theory. I found an old set of notes (http://www.math.toronto.edu/mgualt/Morse%20Theory/mfp.pdf) by Mike Hutchings and these incomplete notes by Ralph Cohen (http://math.stanford.edu/~ralph/morsecourse/biglectures.pdf)

[..I really want a reference which has a detailed description of the “gradient flow line" perspective as in the chater 4,5,6 of Ralph's notes. Just that Ralph's notes are very hard to follow given that all the diagrams are missing!..]

I found this book that has been made legally freely available by the author, https://www3.nd.edu/~lnicolae/Morse2nd.pdf and I have read quite a bit of the old book by Milnor.

• Are there other other good references (particularly lecture/course notes) that I am missing?

Answer 1

If you are looking for the classical approach to Morse theory, I feel nothing beats Milnor's book on the subject:

Milnor, J. Morse theory. Annals of Mathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963

For the Morse homological approach, i.e. counting flowlines, I really like Weber's paper on the subject:

Weber, Joa The Morse-Witten complex via dynamical systems. Expo. Math. 24 (2006), no. 2.

Another standard reference is the book of Banyaga and Hurtubise.

Banyaga, Augustin; Hurtubise, David Lectures on Morse homology. Kluwer Texts in the Mathematical Sciences, 29. Kluwer Academic Publishers Group, Dordrecht, 2004.

A book that is tough to read, but is a gateway to Floer theory is Schwarz' book.

Schwarz, Matthias Morse homology. Progress in Mathematics, 111. Birkhäuser Verlag, Basel, 1993.

I heard good things about the book of Audin and Damian, but I have not read it.

Audin, Michèle; Damian, Mihai Morse theory and Floer homology. Translated from the 2010 French original by Reinie Erné. Universitext. Springer, London; EDP Sciences, Les Ulis, 2014.