I will talk about a special class of submanifolds which play a role in Poisson geometry akin to that of transversals in foliation theory and to that of symplectic submanifolds in Symplectic geometry. The discussion will revolve around normal forms, stability and (non-)existence results.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/5119