TY - JOUR
T1 - Floer homology for almost Hamiltonian isotopies
AU - Banyaga, Augustin
AU - Saunders, Christopher
PY - 2006/3/15
Y1 - 2006/3/15
N2 - Seidel introduced a homomorphism from the fundamental group π1(Ham(M)) of the group of Hamiltonian diffeomorphisms of certain compact symplectic manifolds (M, ω) to a quotient of the automorphism group Aut(HF*(M, ω)) of the Floer homology HF*(M, ω). We prove a rigidity property: If two Hamiltonian loops represent the same element in π1 (Diff(M)), then the image under the Seidel homomorphism of their classes in π1(Ham(M)) coincide. The proof consists in showing that Floer homology can be defined by using 'almost Hamiltonian' isotopies, i.e. isotopies that are homotopic relatively to endpoints to Hamiltonian isotopies.
AB - Seidel introduced a homomorphism from the fundamental group π1(Ham(M)) of the group of Hamiltonian diffeomorphisms of certain compact symplectic manifolds (M, ω) to a quotient of the automorphism group Aut(HF*(M, ω)) of the Floer homology HF*(M, ω). We prove a rigidity property: If two Hamiltonian loops represent the same element in π1 (Diff(M)), then the image under the Seidel homomorphism of their classes in π1(Ham(M)) coincide. The proof consists in showing that Floer homology can be defined by using 'almost Hamiltonian' isotopies, i.e. isotopies that are homotopic relatively to endpoints to Hamiltonian isotopies.
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U2 - 10.1016/j.crma.2006.01.001
DO - 10.1016/j.crma.2006.01.001
M3 - Article
AN - SCOPUS:33644596508
SN - 1631-073X
VL - 342
SP - 417
EP - 420
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 6
ER -