Poisson structures on closed manifolds
Słowa kluczowe
Poisson structures, symplectic foliations, h-principleAbstrakt
We prove an $h$-principle for Poisson structures on closed manifolds. Equivalently, we prove an $h$-principle for symplectic foliations (singular) on closed manifolds. On open manifolds however the singularities could be avoided and it is a known result by Fernandes and Frejlich \cite{Fernandes}.Bibliografia
M. Bertelson, A h-principle for open relations invariant under foliated isotopies, J. Symplectic Geom. 1 (2002), 369–425.
M. Bertelson, Foliations associated to regular Poisson structures, Commun. Contemp. Math. 3 (2001), no. 3, 441–456.
M.S. Borman, Y. Eliashberg and E. Murphy, Existence and classification of overtwisted contact structures in all dimensions, Acta Math. 215 (2015), 215–281.
J.P. Dufour and N.T. Zung, Poisson Structures and Their Normal Forms, Progress in Mathematics, Vol. 242, Birkhäuser, 2005.
Y. Eliashberg and N.M. Mishachev, Wrinkling of smooth mappings and its applications I, Invent. Math. 130 (1997), 349–369.
Y. Eliashberg and N.M. Mishachev, Introduction to the h-Principle, Graduate Studies in Mathematics, Vol. 48, American Mathematical Society, Providence, 2002.
R.L. Fernandes and P. Frejlich, An h-principle for symplectic foliations, Int. Math. Res. Not. IMRN (2012), no. 7, 1505–1518.
M. Gromov, Stable mappings of foliations into manifolds, Izv. Akad. Nauk SSSR Ser. Math. 33 (1069), 707–734 (in Russian).
R. Thom, Les singularités des application différentiables, Ann. Inst. Fourier (Grenoble) 6 (1955/1956), 43–87.
I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Progress in Mathematics, Vol. 118, Birkhäuser, 1994.
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