平凡正则束解流形的一些计算

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-07 DOI:10.1016/j.geomphys.2025.105586

Lapo Rubini

引用次数: 0

摘要

本文计算了具有Kasuya引入的具有分裂型复杂结构的六维正则束的Dolbeault和bot - chern上同调。根据Angella和Kasuya的结果，我们构建了包含在上同调中同构的有限维双子复（CΓ•，•，∂,∂¯）的∧•，•G/Γ，∂,∂¯)。我们把这种双重复合体分解成不可分解的复合体。最后，我们研究了这类流形的形式化概念，给出了在一般复维中∂∂¯-Lemma性质的表征，并在其上计算了三重ABC-Massey积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some computations on trivial canonical-bundle solvmanifolds

We compute the Dolbeault and the Bott-Chern cohomology of six dimensional solvmanifolds endowed with a complex structure of splitting type, introduced by Kasuya, and with trivial canonical bundle. We build, following results by Angella and Kasuya, finite dimensional double subcomplexes

(C_{Γ}^{•, •}, \partial, \bar{\partial}) \subseteq (\land^{•, •} G / Γ, \partial, \bar{\partial})

for which the inclusion is an isomorphism in cohomology. We decompose such double complexes into indecomposable ones. Lastly, we study some notions of formality for this class of manifolds, giving a characterization of the

\partial \bar{\partial}

-Lemma property in general complex dimension, and we compute triple ABC-Massey products on them.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity