In Biran, P., Cornea, O., & Lalonde, F., editors, *Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology*, volume 217, pages 417–438. Kluwer Academic Publishers, Dordrecht, 2006. Series Title: NATO Science Series II: Mathematics, Physics and Chemistry

Paper doi abstract bibtex

Paper doi abstract bibtex

We discuss some recent results on algebraic properties of the group of Hamiltonian diﬀeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of ﬁnitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diﬀeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diﬀeomorphisms.

@incollection{biran_floer_2006, address = {Dordrecht}, title = {{FLOER} {HOMOLOGY}, {DYNAMICS} {AND} {GROUPS}}, volume = {217}, isbn = {978-1-4020-4272-0}, url = {http://link.springer.com/10.1007/1-4020-4266-3_09}, abstract = {We discuss some recent results on algebraic properties of the group of Hamiltonian diﬀeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of ﬁnitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diﬀeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diﬀeomorphisms.}, language = {en}, urldate = {2020-11-13}, booktitle = {Morse {Theoretic} {Methods} in {Nonlinear} {Analysis} and in {Symplectic} {Topology}}, publisher = {Kluwer Academic Publishers}, author = {Polterovich, Leonid}, editor = {Biran, Paul and Cornea, Octav and Lalonde, François}, year = {2006}, doi = {10.1007/1-4020-4266-3_09}, note = {Series Title: NATO Science Series II: Mathematics, Physics and Chemistry}, pages = {417--438}, }

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