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Convexity and Thimm's Trick
Lane, Jeremy...

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Convexity and Thimm's Trick by Lane, Jeremy ( Author )
Lemonjar Open Access
N.A
24-09-2015
In this paper we prove a convexity and fibre-connectedness theorem for proper maps constructed by Thimm's trick on a connected Hamiltonian G-space M that generate a Hamiltonian torus action on an open dense submanifold. Since these maps only generate a Hamiltonian torus action on an open dense submanifold of M, convexity and fibre-connectedness do not follow immediately from Atiyah-Guillemin-Sternberg's convexity theorem, even if M is compact. The core contribution of this paper is to provide a simple argument circumventing this difficulty. In the case where the map is constructed from a chain of subalgebras we prove that the image is given by a list of inequalities that can be computed explicitly. This generalizes the famous example of Gelfand-Zeitlin systems on coadjoint orbits introduced by Guillemin and Sternberg. Moreover, we prove that if such a map generates a completely integrable torus action on an open dense submanifold of M, then all its fibres are smooth embedded submanifolds.
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Article
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English
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MYR 0.01
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https://arxiv.org/abs/1509.07356
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