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Singular Cotangent Bundle Reduction and Polar Actions

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Abstract

A conjecture of Lerman, Montgomery and Sjamaar states that two singular symplectic reductions and are isomorphic if M / G is diffeomorphic to N / H as stratified spaces. We confirm this conjecture under the assumptions that the action \(G\times M\rightarrow M\) is polar with a section N and generalized Weyl group H.

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Acknowledgements

The first author is partially supported by National Natural Science Foundation of China No. 11701427 and Scientific Research Foundation No. 8107144206, Institute for Advanced Study, Tongji University. The second author is partially supported by the Project MYRG2015-00235-FST of the University of Macau. Part of this work was done when both authors were visiting the Institute of Mathematical Sciences in the Chinese University of Hong Kong. We thank Professors Huai-Dong Cao and Naichung Conan Leung for helpful discussion. We also appreciate the referee for valuable suggestions.

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  1. School of Mathematical Sciences, Institute for Advanced Study, Tongji University, Shanghai, China

    Xiaoyang Chen

  2. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China

    Jianyu Ou

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  1. Xiaoyang Chen
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  2. Jianyu Ou
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Correspondence to Jianyu Ou.

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Chen, X., Ou, J. Singular Cotangent Bundle Reduction and Polar Actions. J Geom Anal 30, 3498–3511 (2020). https://doi.org/10.1007/s12220-019-00205-3

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  • DOI: https://doi.org/10.1007/s12220-019-00205-3

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