Symplectic Geometry and Secondary Characteristic Classes
Symplectic Geometry and Secondary Characteristic Classes
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辛几何和次要特征类
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
I. Vaisman
中科院分区：
文献类型：
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作者：
I. Vaisman
这项工作源于对Maslov类(例如(37))的研究，Maslov类是量子物理偏微分方程渐近分析中的一个基本不变量。这类的众多解释之一是由F.Kamber和Ph.Tondeur(43)给出的，它表明Maslov类是复平凡向量丛的次要特征类，赋予其结构群的实约化。在V.I.Arnold关于Maslov类的基础论文(2)中，也没有详细地指出Maslov类是前面提到的向量丛范畴的特征。)因此，我们想要研究这种解释中涉及的所有次要特征类的范围，并且我们在(83)中给出了结果的简短描述。事实证明，对这一理论的完整阐述是相当冗长的，而且，我觉得许多潜在的读者必须使用大量分散的参考文献，才能从辛几何或次要特征类理论中找到必要的信息。另一方面，这两门学科对微分几何和拓扑学以及在物理理论中的应用都有更大的兴趣。
The present work grew out of a study of the Maslov class (e. g. (37]), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many in terpretations of this class was given by F. Kamber and Ph. Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83]. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geome try and topology, and in the applications to physical theories."