Math Papers

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Fredholm theory and transversality for the parametrized and for the S^1-invariant symplectic action
joint work with Alexandru Oancea,
Journal of the European Mathematical Society 12 (2010) no 5, 1181-1229.

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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 L²-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 S¹-invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define S¹-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.

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This paper appeared in Journal of the European Mathematical Society.

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