2014, 21: 80-88. doi: 10.3934/era.2014.21.80

Compactly supported Hamiltonian loops with a non-zero Calabi invariant

1. 

School of Mathematical Sciences, Tel Aviv University, Tel Aviv 6997801, Israel

Received  November 2013 Revised  February 2014 Published  May 2014

We give examples of compactly supported Hamiltonian loops with a non-zero Calabi invariant on certain open symplectic manifolds.
Citation: Asaf Kislev. Compactly supported Hamiltonian loops with a non-zero Calabi invariant. Electronic Research Announcements, 2014, 21: 80-88. doi: 10.3934/era.2014.21.80
References:
[1]

A. Cannas da Silva, Symplectic Toric Manifolds,, 2001. Available from: \url{http://www.math.ist.utl.pt/~acannas/Books/toric.pdf}., ().

[2]

Y. Karshon, Periodic Hamiltonian flows on four-dimensional manifolds,, Memoirs Amer. Math. Soc., 141 (1999). doi: 10.1090/memo/0672.

[3]

D. McDuff, Loops in the Hamiltonian group: A survey,, in Symplectic Topology and Measure Preserving Dynamical Systems, (2010), 127. doi: 10.1090/conm/512/10061.

[4]

D. McDuff and D. Salamon, Introduction to Symplectic Topology,, Second edition, (1998).

[5]

L. Polterovich, The Geometry of the Group of Symplectic Diffeomorphisms,, Lectures in Mathematics ETH Zürich, (2001). doi: 10.1007/978-3-0348-8299-6.

[6]

L. Polterovich, Hamiltonian loops and Arnold's principle,, in Topics in Singularity Theory, (1997), 181.

[7]

S. Seyfaddini, Descent and $C^0$-rigidity of spectral invariants on monotone symplectic manifolds,, J. Top. Anal., 4 (2012), 481. doi: 10.1142/S1793525312500215.

show all references

References:
[1]

A. Cannas da Silva, Symplectic Toric Manifolds,, 2001. Available from: \url{http://www.math.ist.utl.pt/~acannas/Books/toric.pdf}., ().

[2]

Y. Karshon, Periodic Hamiltonian flows on four-dimensional manifolds,, Memoirs Amer. Math. Soc., 141 (1999). doi: 10.1090/memo/0672.

[3]

D. McDuff, Loops in the Hamiltonian group: A survey,, in Symplectic Topology and Measure Preserving Dynamical Systems, (2010), 127. doi: 10.1090/conm/512/10061.

[4]

D. McDuff and D. Salamon, Introduction to Symplectic Topology,, Second edition, (1998).

[5]

L. Polterovich, The Geometry of the Group of Symplectic Diffeomorphisms,, Lectures in Mathematics ETH Zürich, (2001). doi: 10.1007/978-3-0348-8299-6.

[6]

L. Polterovich, Hamiltonian loops and Arnold's principle,, in Topics in Singularity Theory, (1997), 181.

[7]

S. Seyfaddini, Descent and $C^0$-rigidity of spectral invariants on monotone symplectic manifolds,, J. Top. Anal., 4 (2012), 481. doi: 10.1142/S1793525312500215.

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