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Quasi-morphisms and quasi-states in symplectic topology. (English) Zbl 1373.53116
Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. II: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-805-6/hbk; 978-89-6105-803-2/set). 1147-1171 (2014).
Summary: We discuss certain “almost homomorphisms” and “almost linea” functionals that have appeared in symplectic topology and their applications concerning Hamiltonian dynamics, functional-theoretic properties of Poisson brackets and algebraic and metric properties of symplectomorphism groups.
For the entire collection see [Zbl 1314.00104].

53D35 Global theory of symplectic and contact manifolds
53D40 Symplectic aspects of Floer homology and cohomology
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
17B99 Lie algebras and Lie superalgebras
20F69 Asymptotic properties of groups
46L30 States of selfadjoint operator algebras
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