Symplectic quasi-states and semi-simplicity of quantum homology
By Michael Entov, L. Polterovich. 2007
59 citations recorded by the source corpus.
We review and streamline our previous results and the results of Y.Ostrover on the existence of Calabi quasi-morphisms and symplectic quasi-states on symplectic manifolds with semi-simple quantum homology. As an illustration, we discuss the case of symplectic toric Fano 4-manifolds. We present also new results due to D.McDuff: she observed that for the existence of quasi-morphisms/quasi-states it suffices to assume that the quantum homology contains a field as a direct summand, and she showed that this weaker condition holds true for one point blow-ups of non-uniruled symplectic manifolds.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b5516b3f9a7573c82e69efa55d184e74bd07680b
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In Geometry and Topology
- Michael Usher
- L. Polterovich
- F. Zapolsky
- Michael Entov
- E. Shelukhin
- Yong-Geun Oh
- A. Kislev
- V. Ginzburg
In Mathematical Physics
- Michael Usher
- L. Polterovich
- F. Zapolsky
- Michael Entov
- E. Shelukhin
- Yong-Geun Oh
- A. Kislev
- Y. Ostrover
Citations in the corpus
- Quasi-morphisms and the Poisson bracket (2006, background): “alized Hamiltonians F,G∈ C∞(M×[0;1]). We call them stable quasi-morphisms. Example 1.1. The group G is known to carry a stable homogeneous quasimorphism for the following list of symplectic manifolds [5, 7, 15]: complex projective spaces and Grassmannians; CP2 blown up at k≤ 3 points with a symplect”
- Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms (2010, background): “Beginning with [EP03], work of Entov–Polterovich and others has shown that, on some symplectic manifolds, the asymptotic spectral invariant φ̃H 7→ limk→∞ ρ(e;H◊k)0 k (for H normalized and e a well-chosen idempotent with respect to the quantum multiplication ∗0) defines (after multiplication by a con”
- Rigid subsets of symplectic manifolds (2007, background): “In the case when a is the unity in a field that is a direct summand in the decomposition of the K-algebra QH2n(M,ω), as an algebra, into a direct sum of subalgebras, μ is a homogeneous quasi-morphism on H̃am (M) called Calabi quasi-morphism [22],[24],[46]; in the general case it has weaker propertie”