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This text is a version of the lecture notes used during a course at the University of Illinois at Urbana-Champaign in Spring 2012 and a course at the University of Rome ‘La Sapienza’ in Summer 2014, as well as several reading courses. Previous exposure to a course differentiable manifolds is assumed. The aim of the course is to introduce students to the techniques of geometric analysis on manifolds and establish the Atiyah-Singer index theorem.
Course Notes and Supplementary Material (PDF format)
|Course notes||v2 PDF (1.3M)||02/21/17|