### Further Resources

**Books**: The book "

Riemannian Geometry" by M.P. Do Carmo contains significant parts of the material the we will use and cover, including curvature and Jacobi fields (in Chapters 4 and 5), variations on the energy functional and the index theorem (in Chapters 9 and 11). Nevertheless, it does not include the proof of Bott Periodicity, which we will cover. For Morse theory, in addition to J.W. Milnor's textbook, "

An Introduction to Morse Theory" by Y. Matsumoto is a good resource. The first half of "

Morse Theory and Floer Homology " by M. Audin and M. Damian is also a solid reference for finite-dimensional Morse theory. See also "

An Invitation to Morse Theory " by L. Nicolaescu. Further material on Morse homology can be found in "

Lectures on Morse Homology " by A. Banyaga and D. Hurtubise and "

Morse Homology" by M. Schwarz. Finally, for applications of Morse theory for smooth 4-manifolds see "

4-Manifolds and Kirby Calculus" by A.I. Stipsicz and R.E. Gompf and "

4-Manifolds" by S. Akbulut.

**Online resources**:
The lectures on "

Morse Theory" by D. Gay are insightful. There are many available introductory talks online, such as "

this talk" or "

this short introduction".