An index theorem for end-periodic operators

Details An index theorem for end-periodic operators An index theorem for end-periodic operators

2011-05-02

arxiv.org/abs/1105.0260v1

Mathematics

Differential Geometry

50 pages; two color figures

Scientific paper

We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes' Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah-Patodi-Singer eta-invariant in the cylindrical setting.

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