Dirac Operators on Manifolds with Periodic Ends

@inproceedings{Ruberman2007DiracOO,
  title={Dirac Operators on Manifolds with Periodic Ends},
  author={Daniel Ruberman and NIKOLAI SAVELIEV},
  year={2007}
}
This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a necessary and sufficient condition for such an operator to be Fredholm for a generic end-periodic metric. We make use of endperiodic Dirac operators to give an analytical interpretation of an invariant of nonorientable smooth 4-manifolds due to Cappell and Shaneson. From this interpretation we show that some exotic non-orientable 4-manifolds do not admit a metric of positive scalar curvature. 

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