TY - JOUR
T1 - A C0 counterexample to the Arnold conjecture
AU - Buhovsky, Lev
AU - Humilière, Vincent
AU - Seyfaddini, Sobhan
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold (M, ω) must have at least as many fixed points as the minimal number of critical points of a smooth function on M. It is well known that the Arnold conjecture holds for Hamiltonian homeomorphisms of closed symplectic surfaces. The goal of this paper is to provide a counterexample to the Arnold conjecture for Hamiltonian homeomorphisms in dimensions four and higher. More precisely, we prove that every closed and connected symplectic manifold of dimension at least four admits a Hamiltonian homeomorphism with a single fixed point.
AB - The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold (M, ω) must have at least as many fixed points as the minimal number of critical points of a smooth function on M. It is well known that the Arnold conjecture holds for Hamiltonian homeomorphisms of closed symplectic surfaces. The goal of this paper is to provide a counterexample to the Arnold conjecture for Hamiltonian homeomorphisms in dimensions four and higher. More precisely, we prove that every closed and connected symplectic manifold of dimension at least four admits a Hamiltonian homeomorphism with a single fixed point.
KW - Arnold conjecture
KW - C Symplectic geometry
KW - Hamiltonian dynamics
KW - Symplectic and Hamiltonian homeomorphisms
UR - http://www.scopus.com/inward/record.url?scp=85050022175&partnerID=8YFLogxK
U2 - 10.1007/s00222-018-0797-x
DO - 10.1007/s00222-018-0797-x
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AN - SCOPUS:85050022175
SN - 0020-9910
VL - 213
SP - 759
EP - 809
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -