MA726: Differential Geometry II.
Spring 2025

This is a graduate class in differential geometry. This semester the subject is spin geometry. This is the syllabus. Time: T/Th 12:30 PM -- 1:45 PM.
Location: CGS 323

Course schedule and notes

There is not an official textbook for this class, but many topics will follow the presentation of Michelson and Lawson's Spin Geometry (the ``orange book''). I will post lecture notes below in addition to the following standalone summaries:

Notes on Clifford algebra. (Last updated: 2/1)

Notes on the construction of Atiyah, Bott, and Shapiro. (Last updated 2/20)

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Schedule

January 21: Definition of the Clifford algebra. See Notes on Clifford algebra.

January 23: Definition of (S)pin group. Class notes.

January 28: Spin as a universal covering space. Class notes.

January 30: Classification of Clifford algebras. Class notes.

February 4: Clifford modules and spin representations. Class notes.

February 13: Classification of Clifford modules and K-theory. Class notes.

February 20: Complex K-theory, ring structure, Bott periodicity. Class notes .

Problem sets

Problem set 1. Clifford algebras and spin groups (last updated: January 25).

Problem set 2. Some Clifford modules, mostly spin structures (Last updated: February 12).