Mathematical Research Letters
Volume 24 (2017)
Convexity for Hamiltonian torus actions on $b$-symplectic manifolds
Pages: 363 – 377
In [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex $b$-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on $b$-symplectic manifolds. The modular weights of the action on the connected components of the exceptional hypersurface play a fundamental role: either they are all zero and the moment map behaves as in classic symplectic case, or they are all nonzero and the moment map behaves as in the toric $b$-symplectic case studied in [GMPS].
Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia 2016 Prize, by the Ministerio de Economía y Competitividad project with reference MTM2015-69135-P/FEDER and by the Generalitat de Catalunya project with reference 2014SGR634.
Ana Rita Pires was partially supported by a Short Visit Grant from the European Science Foundation’s “Contact and Symplectic Topology” network, and by the National Science Foundation under agreement number DMS-1128155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Received 9 December 2014
Accepted 10 May 2016
Published 24 July 2017