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arXiv · 2110.02679

Symplectic maps and hyperK\"ahler moment map geometry

Yann Rollin
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Abstract

We obtain a correspondence between the group of symplectic diffeomorphisms of a 4-dimensional real torus and the vanishing locus of a certain hyperK\"ahler moment map. This observation gives rise to a new flow, called the modified moment map flow. The construction can be adapted to the polyhedral setting, for which we prove a Duistermaat type theorem. This paper lays out the ground work for some effective polyhedral symplectic geometry and for a potential Morse-Bott theory, with applications to the topology of the space of symplectic maps of the 4-torus.

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Yann Rollin. 2021-10-06. Symplectic maps and hyperK\"ahler moment map geometry. https://arxiv.org/abs/2110.02679

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