Index theory on manifolds with periodic ends

Nikolai Saveliev

http://www.math.miami.edu/~saveliev/

Date(s) : 10/06/2014   iCal
14 h 00 min - 15 h 00 min

We extend the Atiyah-Patodi-Singer index theorem for Dirac type operators from the context of manifolds with product ends to that of manifolds with periodic ends. Our theorem expresses the index in terms of a new end-periodic eta-invariant, which equals the Atiyah-Patodi-Singer eta-invariant in the product end setting. We will also give non-product end examples (associated with Inoue surfaces) and discuss how our index theorem is related to the Seiberg-Witten theory on 4-manifolds with b_1 = 1 and b_2 = 0. This is a joint project with Tom Mrowka and Daniel Ruberman.

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