Log symplectic manifolds and $[Q,R]=0$

Yi Lin; Yiannis Loizides; Reyer Sjamaar; Yanli Song

doi:10.1093/imrn/rnab140

Log symplectic manifolds and $[Q,R]=0$

Symplectic Geometry 2023-11-27 v3

Authors: Yi Lin , Yiannis Loizides , Reyer Sjamaar , Yanli Song

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Abstract

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.

Keywords

log symplectic manifold simple normal crossing stable almost complex structure Spin_c Hamiltonian Dirac operator [Q,R]=0

Cite

@article{arxiv.2008.12728,
  title  = {Log symplectic manifolds and $[Q,R]=0$},
  author = {Yi Lin and Yiannis Loizides and Reyer Sjamaar and Yanli Song},
  journal= {arXiv preprint arXiv:2008.12728},
  year   = {2023}
}

Comments

24 pages, v3: mistake in section 3.2 on minimal coupling corrected, example 3.22 modified

Log symplectic manifolds and $[Q,R]=0$

Abstract

Keywords

Cite

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