Geodesic
First steps in stable Hamiltonian topology
Journal of the European Mathematical Society, Tome 17 (2015) no. 2, pp. 321-404

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DOI

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 S3 is homotopic to a stable Hamiltonian structure which cannot be embedded in R4. 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.
DOI : 10.4171/jems/505
Classification : 53-XX, 00-XX, 37-XX
Keywords: Hamiltonian structure, contact structure, integrable system 
Kai Cieliebak; Evgeny Volkov. First steps in stable Hamiltonian topology. Journal of the European Mathematical Society, Tome 17 (2015) no. 2, pp. 321-404. doi: 10.4171/jems/505
@article{JEMS_2015_17_2_a3,
     author = {Kai Cieliebak and Evgeny Volkov},
     title = {First steps in stable {Hamiltonian} topology},
     journal = {Journal of the European Mathematical Society},
     pages = {321--404},
     year = {2015},
     volume = {17},
     number = {2},
     doi = {10.4171/jems/505},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/505/}
}
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