Cotangent models for group actions on $b$-Poisson manifolds. (arXiv:1811.11894v1 [math.SG])

In this article we give normal forms in a neighbourhood of a compact orbit of a Poisson Lie group action on a $b$-symplectic manifold. In particular we establish cotangent models for Poisson group actions on $b$-Poisson manifolds and a $b$-symplectic slice theorem. We examine interesting particular instances of Poisson-Lie group actions on $b$-symplectic manifolds. Also, we revise the notion of cotangent lift and twisted $b$-cotangent lift introduced in \cite{km} and provide a generalization of the twisted $b$-cotangent lift to higher dimensional torus actions. We introduce the notion of $b$-Lie group and the associated $b$-symplectic structures in its $b$-cotangent bundle together with their reduction theory. 查看全文>>