CALABI QUASIMORPHISMS FOR THE SYMPLECTIC BALL
2004 ◽
Vol 06
(05)
◽
pp. 793-802
◽
Keyword(s):
We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms. In addition these quasimorphisms are Lipschitz in the Hofer metric and have the following property: the value of each such quasimorphism on any symplectomorphism supported in any "sufficiently small" open subset of the ball equals the Calabi invariant of the symplectomorphism. By a "sufficiently small" open subset we mean that it can be displaced from itself by a symplectomorphism of the ball. As a byproduct we show that the (Lagrangian) Clifford torus in the complex projective space cannot be displaced from itself by a Hamiltonian isotopy.
2007 ◽
Vol 09
(06)
◽
pp. 769-780
◽
2020 ◽
Vol 17
(5)
◽
pp. 744-747
2002 ◽
Vol 66
(3)
◽
pp. 465-475
◽
1998 ◽
Vol 14
(1)
◽
pp. 1-8
◽
Keyword(s):
1993 ◽
Vol 114
(3)
◽
pp. 443-451