Dirac operators on manifolds with periodic ends
几何拓扑
2007-05-23 v4 微分几何
摘要
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.
引用
@article{arxiv.math/0702271,
title = {Dirac operators on manifolds with periodic ends},
author = {Daniel Ruberman and Nikolai Saveliev},
journal= {arXiv preprint arXiv:math/0702271},
year = {2007}
}
备注
22 pages. Additional references and acknowledgements added