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

Yi Lin
, Yiannis Loizides
, Reyer Sjamaar
, Yanli Song

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	14034-14066
Number of pages	33
Journal	International Mathematics Research Notices
Volume	2022
Issue number	18
DOIs	https://doi.org/10.1093/imrn/rnab140
State	Published - Sep 1 2022

Scopus Subject Areas

General Mathematics

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10.1093/imrn/rnab140

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title = "Log Symplectic Manifolds and [Q , R ] = 0",

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 Spinc. In the compact Hamiltonian case we prove that the index of the Spinc Dirac operator twisted by a prequantum line bundle satisfies a [Q, R] = 0 theorem.",

author = "Yi Lin and Yiannis Loizides and Reyer Sjamaar and Yanli Song",

year = "2022",

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T1 - Log Symplectic Manifolds and [Q , R ] = 0

AU - Lin, Yi

AU - Loizides, Yiannis

AU - Sjamaar, Reyer

AU - Song, Yanli

PY - 2022/9/1

Y1 - 2022/9/1

N2 - 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 Spinc. In the compact Hamiltonian case we prove that the index of the Spinc Dirac operator twisted by a prequantum line bundle satisfies a [Q, R] = 0 theorem.

AB - 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 Spinc. In the compact Hamiltonian case we prove that the index of the Spinc Dirac operator twisted by a prequantum line bundle satisfies a [Q, R] = 0 theorem.

UR - https://www.scopus.com/pages/publications/85158054658

U2 - 10.1093/imrn/rnab140

DO - 10.1093/imrn/rnab140

M3 - Article

AN - SCOPUS:85158054658

SN - 1073-7928

VL - 2022

SP - 14034

EP - 14066

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 18

ER -

Log Symplectic Manifolds and [Q , R ] = 0

Abstract

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