Published in Journal of Gökova Geometry Topology, Volume 1 (2007)
Title Dirac operators on manifolds with periodic ends
Author Daniel Ruberman and Nikolai Saveliev
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 end-periodic Dirac operators to give an analytical interpretation of an invariant of non-orientable 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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Submitted: April 12, 2007
Revised: September 12, 2007
Accepted: September 14, 2007
 Journal of GGT Volume 1

Last updated: December 2007
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