Contact Reduction
Contact Reduction
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DOI：
10.1090/s0002-9947-02-03045-3
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发表时间：
2001-04
期刊：
影响因子：
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通讯作者：
Christopher Willett
中科院分区：
文献类型：
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作者：
Christopher Willett
.在这篇文章中，我提出了一个新的方法来减少一个共同定向的接触流形M配备了一个李群G的作用的接触变换。在一定的正则性和完整性假设下，接触商M μ at μ ∈ g μ是一个自然的共定向接触轨道，它与用来表示给定接触结构的接触形式无关。去除正则性和完整性假设，并将其替换为满足紧致对称群的关于切片存在的假设，得到接触艾德空间;即，配备有线丛的艾德空间，当限制到每个层时，定义了共定向接触结构。这是作者和E. Lerman（[LW]）.
. In this article I propose a new method for reducing a co-oriented contact manifold M equipped with an action of a Lie group G by contact transformations. With a certain regularity and integrality assumption the contact quotient M µ at µ ∈ g ∗ is a naturally a co-oriented contact orbifold which is independent of the contact form used to represent the given contact structure. Removing the regularity and integrality assumptions and replacing them with one concerning the existence of a slice, which is satisfied for compact symmetry groups, results in a contact stratified space; i.e, a stratified space equipped with a line bundle which, when restricted to each stratum, defines a co-oriented contact structure. This extends the previous work of the author and E. Lerman ([LW]).