Seidel's Representation on the Hamiltonian Group of a Cartesian Product
Facultad de Ciencias y CUICBAS, Universidad de Colima, Bernal Díaz del Castillo No. 340, Colima, Col., Mexico 28045
Correspondence: Correspondence to be sent to: andres_pedroza{at}ucol.mx
Let 
be a closed symplectic manifold and 
the group of Hamiltonian diffeomorphisms of 
. Then the Seidel homomorphism is a map from the fundamental group of 
to the quantum homology ring 
. Using this homomorphism, we give a sufficient condition for when a nontrivial loop 
in 
determines a nontrivial loop 
in 
, where 
is a closed symplectic manifold such that 
.
References
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- McDuff D. Quantum homology of fibrations over
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of symplectic automorphism groups and invertibles in quantum homology rings. Geometric and Functional Analysis (1997) 7:1046–96.[CrossRef][ISI] - Weinstein A. Cohomology of symplectomorphism groups and critical values of Hamiltonian. Mathematische Zeitschrift (1989) 210:75–82.
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