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In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group actions on b-symplectic manifolds.
We prove that the half-wave maps problem on R4+1 with target S2 is globally well-posed for smooth initial data which are small in the critical l1 based Besov space. This is a formal analogue of the result [17].