Volume 6, issue 1 (2006)

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Calabi quasi-morphisms for some non-monotone symplectic manifolds

Yaron Ostrover

Algebraic & Geometric Topology 6 (2006) 405–434
 arXiv: math.SG/0508090
Abstract

In this work we construct Calabi quasi-morphisms on the universal cover $\stackrel{˜}{Ham}\left(M\right)$ of the group of Hamiltonian diffeomorphisms for some non-monotone symplectic manifolds. This complements a result by Entov and Polterovich which applies in the monotone case. Moreover, in contrast to their work, we show that these quasi-morphisms descend to non-trivial homomorphisms on the fundamental group of $Ham\left(M\right)$.

Keywords
symplectic manifolds, Hamiltonian diffeomorphisms, Quantum homology, Calabi quasi-morphisms
Mathematical Subject Classification 2000
Primary: 53D05, 53D12, 53D45
Secondary: 20F69