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.Comment: 15 pages; v2: the title was changed; v3: proof of Lemma 2 was
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