First steps in stable Hamiltonian topology

Cieliebak, Kai, and Volkov, Evgeny. "First steps in stable Hamiltonian topology." Journal of the European Mathematical Society 017.2 (2015): 321-404. <http://eudml.org/doc/277213>.

@article{Cieliebak2015,
abstract = {In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on $S^3$ is homotopic to a stable Hamiltonian structure which cannot be embedded in $\mathbb \{R\}^4$. Moreover, we derive a structure theorem for stable Hamiltonian structures in dimension three, study sympectic cobordisms between stable Hamiltonian structures, and discuss implications for the foundations of symplectic field theory.},
author = {Cieliebak, Kai, Volkov, Evgeny},
journal = {Journal of the European Mathematical Society},
keywords = {Hamiltonian structure; contact structure; integrable system; stable Hamiltonian topology; stable Hamiltonian topology},
language = {eng},
number = {2},
pages = {321-404},
publisher = {European Mathematical Society Publishing House},
title = {First steps in stable Hamiltonian topology},
url = {http://eudml.org/doc/277213},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Cieliebak, Kai
AU - Volkov, Evgeny
TI - First steps in stable Hamiltonian topology
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 2
SP - 321
EP - 404
AB - In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on $S^3$ is homotopic to a stable Hamiltonian structure which cannot be embedded in $\mathbb {R}^4$. Moreover, we derive a structure theorem for stable Hamiltonian structures in dimension three, study sympectic cobordisms between stable Hamiltonian structures, and discuss implications for the foundations of symplectic field theory.
LA - eng
KW - Hamiltonian structure; contact structure; integrable system; stable Hamiltonian topology; stable Hamiltonian topology
UR - http://eudml.org/doc/277213
ER -