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http://dx.doi.org/10.4134/BKMS.b210406

ON TORIC HAMILTONIAN T-SPACES WITH ANTI-SYMPLECTIC INVOLUTIONS  

Kim, Jin Hong (Department of Mathematics Education Chosun University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.3, 2022 , pp. 671-683 More about this Journal
Abstract
The aim of this paper is to deal with the realization problem of a given Lagrangian submanifold of a symplectic manifold as the fixed point set of an anti-symplectic involution. To be more precise, let (X, ω, µ) be a toric Hamiltonian T-space, and let ∆ = µ(X) denote the moment polytope. Let τ be an anti-symplectic involution of X such that τ maps the fibers of µ to (possibly different) fibers of µ, and let p0 be a point in the interior of ∆. If the toric fiber µ-1(p0) is real Lagrangian with respect to τ, then we show that p0 should be the origin and, furthermore, ∆ should be centrally symmetric.
Keywords
T-spaces; anti-symplectic involutions; moment polytopes; conjugations; quasitoric manifolds; small covers; real Lagrangians;
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