Notes on the Atiyah-Singer Index Theorem
by Liviu I. Nicolaescu
Publisher: University of Notre Dame 2005
Number of pages: 135
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
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The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.
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