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On the complex structure of symplectic quotients

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Science China Mathematics 2021年第12期64卷 2719-2742页

作者： Xiangsheng Wang Beijing International Center for Mathematical Research Peking UniversityBeijing 100871China School of Mathematics Shandong UniversityJinan 250100China

Let K be a compact *** a symplectic quotient M_(λ) of a compact Hamiltonian Kahler K-manifold,we show that the induced complex structure on M_(λ) is locally invariant when the parameter λ varies in Lie(K)^(*).To prove such a result,we take two di erent approaches:(i)use the complex geometry properties of the symplectic implosion construction;(ii)investigate the variation of geometric invariant theory(GIT)quotients.

关键词： complex structure symplectic reduction symplectic implosion geometric invariant theory

Hormander index in finite-dimensional case

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Frontiers of Mathematics in China 2018年第3期13卷 725-761页

作者： Yuting ZHOU Li WU Chaofeng ZHU Chern Institute of Mathematics and LPMC Nankai University Tianjin 300071 China Department of Mathematics Shandong University Jinan 250100 China

We calculate the Hormander index in the finite-dimensional case. Then we use the result to give some iteration inequalities, and prove almost existence of mean indices for given complete autonomous Hamiltonian system on compact symplectic manifold with symplectic trivial tangent bundle and given autonomous Hamiltonian system on regular compact energy hypersurface of symplectic manifold with symplectic trivial tangent bundle.

关键词： Maslov index HSrmander index Maslov-type index symplectic reduction

K-Theory and the Quantization Commutes with reduction Problem

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Chinese Annals of Mathematics,Series B 2014年第5期35卷 703-732页

作者： Nigel HIGSON Yanli SONG Department of Mathematics Pennsylvania State University University Park Department of Mathematics University of TorontoRoom 6290 40 St. George Street Toronto OntarioCanada M5S2E4

The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They develop the machinery of K-theory wrong-way maps in the context of orbifolds and use it to relate the quantization commutes with reduction phenomenon to Bott periodicity and the K-theory formulation of the Weyl character formula.

关键词： symplectic reduction Quantization K-Theory K-Homology CompactLie groups

Gluing Affine Vortices

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Acta Mathematica Sinica,English Series 2024年第1期40卷 250-312页

作者： Guang Bo XU Department of Mathematics Rutgers UniversityHill Center-Busch Campus 110 Frelinghuysen RoadPiscatawayNJ 08854-8019USA

We provide an analytical construction of the gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary *** result is a necessary ingredient in studies of the relation between gauged ... 详细信息

关键词： Affine vortices gauged linear sigma model adiabatic limit symplectic reduction

The Moduli Space in the Gauged Linear Sigma Model

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Chinese Annals of Mathematics,Series B 2017年第4期38卷 913-936页

作者： Huijun FAN Tyler JARVIS Yongbin RUAN School of Mathematical Sciences Peking University Beijing 100871 China. Department of Mathematics Brigham Young University Provo UT 84602 USA. Department of Mathematics University of Michigan Ann Arbor MI 48105 USA.

This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors... 详细信息

关键词： Landau-Ginzburg Calabi-Yau Gromov-Witten GLSM Moduli Phase Variation of geometric invariant theory symplectic reduction