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}., ().   Google Scholar

[2]

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

[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.  Google Scholar

[4]

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

[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.  Google Scholar

[6]

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

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

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}., ().   Google Scholar

[2]

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

[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.  Google Scholar

[4]

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

[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.  Google Scholar

[6]

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

[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.  Google Scholar

[1]

Z. Reichstein and B. Youssin. Parusinski's "Key Lemma" via algebraic geometry. Electronic Research Announcements, 1999, 5: 136-145.

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