不可定向曲面上Yang-Mills理论的可定向性
Orientability in Yang-Mills Theory over Nonorientable Surfaces
摘要：
在arXiv：math/0605587中，前两位作者在连通的、闭的、不可定向曲面上的主U（n）-丛的联络空间上构造了规范等变Morse分层。这个空间可以用这个丛在这个不可定向曲面的可定向双重覆盖上的拉回上的联络空间的实轨迹来标识。在此上下文中，Morse地层的法丛是实向量丛。我们证明了当不可定向曲面不同胚于Klein瓶时，这些丛及其相关的同伦轨道丛对任意n是可定向的;当不可定向曲面是克莱因瓶时，对n<4，这些丛及其相关的同伦轨道丛是可定向的.当结构群为SU（n）时，我们也得到了类似的定向性结果.
英文摘要：
In arXiv:math/0605587, the first two authors have constructed a gauge-equivariant Morse stratification on the space of connections on a principal U(n)-bundle over a connected, closed, nonorientable surface. This space can be identified with the real locus of the space of connections on the pullback of this bundle over the orientable double cover of this nonorientable surface. In this context, the normal bundles to the Morse strata are real vector bundles. We show that these bundles, and their associated homotopy orbit bundles, are orientable for any n when the nonorientable surface is not homeomorphic to the Klein bottle, and for n<4 when the nonorientable surface is the Klein bottle. We also derive similar orientability results when the structure group is SU(n).
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