Seidel's Representation on the Hamiltonian Group of a Cartesian Product

@article{Pedroza2008SeidelsRO,
  title={Seidel's Representation on the Hamiltonian Group of a Cartesian Product},
  author={Andr{\'e}s Pedroza},
  journal={arXiv: Symplectic Geometry},
  year={2008}
}
  • Andrés Pedroza
  • Published 2008
  • Mathematics
  • arXiv: Symplectic Geometry
  • Let $(M,\omega)$ be a closed symplectic manifold and $\textup{Ham}(M,\omega)$ the group of Hamiltonian diffeomorphisms of $(M,\omega)$. Then the Seidel homomorphism is a map from the fundamental group of $\textup{Ham}(M,\omega)$ to the quantum homology ring $QH_*(M;\Lambda)$. Using this homomorphism we give a sufficient condition for when a nontrivial loop $\psi$ in $\textup{Ham}(M,\omega)$ determines a nontrivial loop $\psi\times\textup{id}_N$ in $\textup{Ham}(M\times N,\omega\oplus\eta… CONTINUE READING

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