Joyce 广义 Kummer 构造中的结合子流形

Joyce 广义 Kummer 构造中的余结合子流形

Coassociative submanifolds in Joyce's generalised Kummer constructions

本文研究 Joyce 广义 Kummer 构造所得 $G_2$ 流形，在度量退化的临界区域构造余结合子流形，并证明其体积在轨形极限下趋于零。

${\rm G}_2$-instantons on generalised Kummer constructions

In this article we introduce a method to construct $\rm{G}_2$-instantons on $\rm{G}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on $\rm{G}_2$-orbifolds of the form $T^7/ Γ$. We use this construction to produce non-trivial examples of $\rm{G}_2$-instantons.

Computing $ν$-invariants of Joyce's compact $G_2$-manifolds

Crowley and Nordström introduced an invariant of $G_2$-structures on the tangent bundle of a closed 7-manifold, taking values in the integers modulo 48. Using the spectral description of this invariant due to Crowley, Goette and Nordström, we compute it for many of the closed torsion-free $G_2$-manifolds defined by Joyce's generalized Kummer construction.

广义 Kummer 构造上的一族光滑 $G_2$-瞬子

A smooth family of $G_2$-instantons over a generalised Kummer construction

本文在广义 Kummer 构造上利用 $\mathbb{Z}_2$-作用克服障碍，构造了首个紧致 $G_2$-流形上光滑 1-参数 $G_2$-瞬子族，并证明其无穷小刚性、非平坦及规范非等价性。

锥形奇点的关联子流形的变形与去奇处理

Deformations and desingularizations of conically singular associative submanifolds

本文研究了关联子流形退化为锥形奇点的过渡，证明了相关稳定性指数及去奇处理结果。

On the Global Structure of Some Natural Fibrations of Joyce Manifolds

The study of fibrations of the target manifolds of string/M/F-theories has provided many insights to the dualities among these theories or even as a tool to build up dualities since the work of Strominger, Yau, and Zaslow on the Calabi-Yau case. For M-theory compactified on a Joyce manifold $M^7$, the fact that $M^7$ is constructed via a generalized Kummer construction on a 7-torus ${\smallBbb T}^7$ with a torsion-free $G_2$-structure $ϕ$ suggests that there are natural fibrations of $M^7$ by ${\smallBbb T}^3$, ${\smallBbb T}^4$, and K3 surfaces in a way governed by $ϕ$. The local picture of s…