Dirac operators on manifolds with periodic ends

Details Dirac operators on manifolds with periodic ends Dirac operators on manifolds with periodic ends

2007-02-09

arxiv.org/abs/math/0702271v4

Mathematics

Geometric Topology

22 pages. Additional references and acknowledgements added

Scientific paper

This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a sufficient condition for such an operator to be Fredholm for a generic end-periodic metric; this condition is shown to be necessary in dimension 4. 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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