arXiv 1104.40842011-04math.SGmath.DG

微分空间、向量场与轨道型分层

Differential Spaces, Vector Fields, and Orbit-Type Stratifications

Jordan Watts

备注：: 44 pages. Earlier versions of this paper were supposed to prove a result regarding a de Rham complex of differential forms on the symplectic quotient. A crucial lemma in the proof was incorrect. The theory used remains useful for studying the stratifications mentioned in the abstract from the point of view of differential spaces. Erroneous parts removed

摘要：

设$G$是李群，$(M,ω)$是辛流形.若$G$在具有动量映射$μ$的$(M,ω)$上有Hamilton作用，则$M$、$μ$的零水平集、轨道空间和相应的辛商都有诱导分层.我们把这个设置到微分空间的语言，作为一个结果，我们发现，分层是内在的环的光滑函数在每个空间。

英文摘要：

Let $G$ be a Lie group, and let $(M,ω)$ be a symplectic manifold. If $G$ admits a Hamiltonian action on $(M,ω)$ with momentum map $μ$, then $M$, the zero-level set of $μ$, the orbit space, and the corresponding symplectic quotient all have induced stratifications. We push this setting into the language of differential spaces, and as a consequence we find that the stratifications are intrinsic to the ring of smooth functions on each space.

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摘要：

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