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Title:
End-Periodic Index Theory
Speaker:
Abstract:
The Atiyah-Patodi-Singer index theorem calculates the index of anelliptic differential operator on a manifold with boundary, subject to certain boundary conditions that arise naturally in geometry and topology. In many circumstances, these give rise to an index problem on a manifold with product ends. I will discuss joint work with Tom Mrowka and Nikolai Saveliev on a generalization to the setting of manifolds with periodic ends and the connection with problems in 4-dimensional topology. I will also discuss the simplest version of the periodic index theorem, namely the Gauss-Bonnet theorem, where the difference between the periodic and product
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