The normal form theorem around Poisson transversals

Pedro Frejlich and Ioan Mărcuţ

Vol. 287 (2017), No. 2, 371–391

DOI: 10.2140/pjm.2017.287.371

Abstract

We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein’s symplectic neighborhood theorem from symplectic geometry and Weinstein’s splitting theorem. Our approach turns out to be essentially canonical, and as a byproduct, we obtain an equivariant version of the latter theorem.

Dedicated to Alan Weinstein on the occasion of his 70th birthday

Keywords

differential geometry, symplectic geometry, Poisson manifolds, Poisson groupoids and algebroids

Mathematical Subject Classification 2010

Primary: 53D17

Secondary: 53D05

Milestones

Received: 18 January 2016

Revised: 11 July 2016

Accepted: 29 August 2016

Published: 9 March 2017