Poisson structures on closed manifolds

Sauvik Mukherjee

DOI: http://dx.doi.org/10.12775/TMNA.2017.059

Abstract


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}.

Keywords


Poisson structures; symplectic foliations; h-principle

Full Text:

PREVIEW FULL TEXT

References


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.


Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism