Topology of Almost Complex Structures on Six-Manifolds

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-07-26 DOI:10.3842/SIGMA.2022.093
Gustavo Granja, A. Milivojević
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Abstract

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures.
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六流形上几乎复杂结构的拓扑
我们研究了封闭六维流形上的(正交)几乎复结构空间作为给定度规的扭转空间的截面空间。对于具有消失第一Betti数的连通六流形,我们用一个圆作用将几乎复杂结构的空间表示为该流形上七球束截面空间的商,然后利用这一描述计算出满足一定陈氏数条件的分量的有理同伦理论极小模型。在此基础上,我们进一步得到了关于相应的几乎复杂结构的Chern类的扭转空间两段的同调交数的公式。
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
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