Dirac operators on manifolds with periodic ends

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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.
22 pages. Additional references and acknowledgements added

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Geometric Topology, Differential Geometry, 57R57; 58J20

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http://salesiana.dossiersoluciones.com/handle/123456789/127167

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702271
 http://arxiv.org/abs/math/0702271

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arXiv