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