Calabi quasi-morphisms for some non-monotone symplectic manifolds

Ostrover, Yaron

doi:10.2140/agt.2006.6.405

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Calabi quasi-morphisms for some non-monotone symplectic manifolds

Yaron Ostrover

Algebraic & Geometric Topology 6 (2006) 405–434

DOI: 10.2140/agt.2006.6.405

arXiv: math.SG/0508090

Abstract

In this work we construct Calabi quasi-morphisms on the universal cover $\tilde{Ham} (M)$ 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 $Ham (M)$ .

Keywords

symplectic manifolds, Hamiltonian diffeomorphisms, Quantum homology, Calabi quasi-morphisms

Mathematical Subject Classification 2000

Primary: 53D05, 53D12, 53D45

Secondary: 20F69

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Publication

Received: 9 September 2005

Accepted: 15 February 2006

Published: 12 March 2006

Authors

Yaron Ostrover
School of Mathematical Sciences Tel Aviv University 69978 Tel Aviv Israel

Volume 6, issue 1 (2006)