2022/09/28 by Cavalcanti, Gil R., Marcut, Ioan
#53D10 (secondary) #53D17 (primary) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2209.14016
We explicitly construct several Poisson structures with compact support. For example, we show that any Poisson structure on \Rn with polynomial coefficients of degree at most two can be modified outside an open ball, such that it becomes compactly supported. We also show that a symplectic manifold with either contact or cosymplectic boundary admits a Poisson structure which vanishes to infinite order at the boundary and agrees with the original symplectic structure outside an arbitrarily small tubular neighbourhood of the boundary. As a consequence, we prove that any even-dimensional manifold admits a Poisson structure which is symplectic outside a codimension one subset.