Ebook Download | Spin Geometry | As a graduate student in mathematics I survived on this encyclopedic work. Anyone interested in differential geometry or differential topology will eventually need something in this book. Prerequisites are graduate-level algebra and analysis, and some topology and differential geometry. He introduces the subject of pseudodifferential operators and Sobolev spaces, but it's easy to get lost in that part unless you first read Shubin's book "Pseudodifferential operators and Spectral theory". Also, the quick shuffling of Lie group information can be disheartening if you're not used to it. Harvey's book "Spinors and Calibrations" is a more elementary book if this is the case.
This book touches on many important topics like the Atiyah-Singer Index Theorem, the Bochner method, Riemann-Roch, and mathematical physics, but you will probably want to supplement your reading with individual books on each of these topics.
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