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- W3204407896 abstract "We provide an interpretation of the space of symplectic diffeomorphism of a 4-dimensional real torus $T^4$, as the vanishing locus of a hyperKahler moment map. This construction leads to a notion of modified hyperKahler moment map flow, whose regular fixed points coincide with the symplectic diffeomorphisms of $T^4$ . Given a Euclidean triangulation of $T^4$ , we introduce a notion of polyhedral maps and polyhedral symplectic maps of the torus. We show that all the construction carried out in the smooth setting have analogues in the polyhedral setting. In this context, the hyperKahler modified moment map flow is an ordinary differential equation, which is always convergent. Under a non-degeneracy assumption of the limit, this provides an effective construction of polyhedral symplectic maps of the torus. This paper lays out the ground work for some experimental symplectic geometry. In an upcoming work with Franc{c}ois Jauberteau, we write a computer program that runs a numerical version of the flow and generates non trivial examples of symplectic polyhedral maps of $T^4$." @default.
- W3204407896 created "2021-10-11" @default.
- W3204407896 creator A5032412764 @default.
- W3204407896 date "2021-10-06" @default.
- W3204407896 modified "2023-09-27" @default.
- W3204407896 title "Polyhedral symplectic maps and hyperKahler geometry" @default.
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