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arXiv · 1104.4084

Differential Spaces, Vector Fields, and Orbit-Type Stratifications

Jordan Watts
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Abstract

Let $G$ be a Lie group, and let $(M,\omega)$ be a symplectic manifold. If $G$ admits a Hamiltonian action on $(M,\omega)$ with momentum map $\mu$, then $M$, the zero-level set of $\mu$, 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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Jordan Watts. 2011-04-20. Differential Spaces, Vector Fields, and Orbit-Type Stratifications. https://arxiv.org/abs/1104.4084

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