Fredholm theory and transversality for the parametrized and for the $S^1$-invariant symplectic action

Bourgeois, Frédéric, and Oancea, Alexandru. "Fredholm theory and transversality for the parametrized and for the $S^1$-invariant symplectic action." Journal of the European Mathematical Society 012.5 (2010): 1181-1229. <http://eudml.org/doc/277404>.

@article{Bourgeois2010,
abstract = {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.},
author = {Bourgeois, Frédéric, Oancea, Alexandru},
journal = {Journal of the European Mathematical Society},
keywords = {Hamiltonian action functional; Fredholm property; Floer homology; Hamiltonian action functional; Fredholm property; Floer homology},
language = {eng},
number = {5},
pages = {1181-1229},
publisher = {European Mathematical Society Publishing House},
title = {Fredholm theory and transversality for the parametrized and for the $S^1$-invariant symplectic action},
url = {http://eudml.org/doc/277404},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Bourgeois, Frédéric
AU - Oancea, Alexandru
TI - Fredholm theory and transversality for the parametrized and for the $S^1$-invariant symplectic action
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 5
SP - 1181
EP - 1229
AB - 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.
LA - eng
KW - Hamiltonian action functional; Fredholm property; Floer homology; Hamiltonian action functional; Fredholm property; Floer homology
UR - http://eudml.org/doc/277404
ER -