Fredholm theory and transversality for the parametrized and for the $S^1$-invariant symplectic action - Mathematics > Symplectic GeometryReport as inadecuate




Fredholm theory and transversality for the parametrized and for the $S^1$-invariant symplectic action - Mathematics > Symplectic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study the parametrized Hamiltonian action functional forfinite-dimensional families of Hamiltonians. We show that the linearizedoperator for the $L^2$-gradient lines is Fredholm and surjective, for a genericchoice of Hamiltonian and almost complex structure. We also establish theFredholm property and transversality for generic $S^1$-invariant families ofHamiltonians and almost complex structures, parametrized by odd-dimensionalspheres. This is a foundational result used to define $S^1$-equivariant Floerhomology. As an intermediate result of independent interest, we generalizeAronszajn-s unique continuation theorem to a class of ellipticintegro-differential inequalities of order two.



Author: Frédéric Bourgeois, Alexandru Oancea

Source: https://arxiv.org/







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