g2流形的环面几何

IF 2 1区 数学
T. Madsen, A. Swann
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引用次数: 11

摘要

对于一个或多个定义形式,我们考虑具有多重哈密顿有效环面作用的g2流形。发现t3行动的情况是有区别的。对于这类动作,在三形式和四形式下都是多重哈密顿的,我们得到了一个Gibbons-Hawking型解,给出了开密集合上的几何形状,表示函数的对称3×3-matrix。这就产生了一些特别简单的完整度等于G2的显式度量的例子。我们证明了多矩映射在拓扑上将全轨道空间表现为一个光滑的四流形,其中包含一个三价图作为特殊轨道集的像,并在一些完整的例子中描述了这些图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Toric geometry of G2–manifolds
We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz giving the geometry on an open dense set in terms a symmetric 3×3-matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to G2. We prove that the multi-moment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.
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来源期刊
Geometry & Topology
Geometry & Topology 数学-数学
自引率
5.00%
发文量
34
期刊介绍: Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
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