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Index theory on end-periodic manifolds

Presented by: 
N Saveliev University of Miami
Monday 23rd March 2015 - 10:00 to 11:00
INI Seminar Room 1
Co-authors: Tomasz Mrowka (MIT), Daniel Ruberman (Brandeis University)

End-periodic manifolds are non-compact Riemannian manifolds whose ends are modeled on an infinite cyclic cover of a closed manifold; an important special case are manifolds with cylindrical ends. We extend some of the classical index theorems to this setting, including the Atiyah-Patodi-Singer theorem computing the index of Dirac-type operators. Our theorem expresses this index in terms of a new periodic eta-invariant which equals the classical eta-invariant in the cylindrical end setting.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons