Quasi-morphisms and the Poisson bracket
| dc.creator | Entov, Michael | |
| dc.creator | Polterovich, Leonid | |
| dc.creator | Zapolsky, Frol | |
| dc.date | 2006-05-15 | |
| dc.date | 2007-07-15 | |
| dc.date.accessioned | 2026-07-07T08:17:27Z | |
| dc.date.available | 2026-07-07T08:17:27Z | |
| dc.description | For a class of symplectic manifolds, we introduce a functional which assigns a real number to any pair of continuous functions on the manifold. This functional has a number of interesting properties. On the one hand, it is Lipschitz with respect to the uniform norm. On the other hand, it serves as a measure of non-commutativity of functions in the sense of the Poisson bracket, the operation which involves first derivatives of the functions. Furthermore, the same functional gives rise to a non-trivial lower bound for the error of the simultaneous measurement of a pair of non-commuting Hamiltonians. These results manifest a link between the algebraic structure of the group of Hamiltonian diffeomorphisms and the function theory on a symplectic manifold. The above-mentioned functional comes from a special homogeneous quasi-morphism on the universal cover of the group, which is rooted in the Floer theory. | |
| dc.description | minor changes, to appear in Pure and Applied Mathematics Quarterly (special issue dedicated to Gregory Margulis' 60th birthday) | |
| dc.identifier | https://arxiv.org/abs/math/0605406 | |
| dc.identifier | http://arxiv.org/abs/math/0605406 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134094 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 53D35, 53D40, 53D05 | |
| dc.title | Quasi-morphisms and the Poisson bracket | |
| dc.type | text |