Log Symplectic Manifolds and [Q,R]=0

  title={Log Symplectic Manifolds and [Q,R]=0},
  author={Yi Lin and Yiannis Loizides and Reyer Sjamaar and Yanli Song},
  journal={International Mathematics Research Notices},
We show, under an orientation hypothesis, that a log symplectic manifold with simple normal crossing singularities has a stable almost complex structure, and hence is Spin$_c$. In the compact Hamiltonian case we prove that the index of the Spin$_c$ Dirac operator twisted by a prequantum line bundle satisfies a $[Q,R]=0$ theorem. 



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