Geodesic
Fredholm theory and transversality for the parametrized and for the $S_1$-invariant symplectic action
Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1181-1229 Cet article a éte moissonné depuis la source EMS Press

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We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the _L_2-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic _S_1-invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define _S_1-equivariant Floer homology. As an intermediate result of independent interest, we generalize Aronszajn’s unique continuation theorem to a class of elliptic integro-differential inequalities of order two.
DOI : 10.4171/jems/227
Classification : 53-XX, 00-XX, 55-XX, 58-XX 
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     author = {Fr\'ed\'eric Bourgeois and Alexandru Oancea},
     title = {Fredholm theory and transversality for the parametrized and for the $S_1$-invariant symplectic action},
     journal = {Journal of the European Mathematical Society},
     pages = {1181--1229},
     year = {2010},
     volume = {12},
     number = {5},
     doi = {10.4171/jems/227},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/227/}
}
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Frédéric Bourgeois; Alexandru Oancea. Fredholm theory and transversality for the parametrized and for the $S_1$-invariant symplectic action. Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1181-1229. doi: 10.4171/jems/227

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