由耳环缠结在枕套上引起的对应关系

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2022-11-11 DOI:10.1112/topo.12272

Guillem Cazassus, Christopher Herald, Paul Kirk, Artem Kotelskiy

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引用次数: 2

摘要

耳环缠结由四根线组成4 pt × I∧s2 × I$ 4\text{pt} \乘以I \子集S^2 \乘以I$和一条围绕其中一根线的子午线。用一个非平凡的SO(3)$ SO(3)$束来装备这个缠结，我们证明了它的无迹SU(2)$ SU(2)$平坦模空间在拓扑上是光滑的三格曲面。我们还证明了从该表面到耳环缠结边界的无迹平面模空间的限制映射是两个枕套的特定拉格朗日浸入积。后一种计算表明，数字8冒泡——由Bottman和Wehrheim预测的一种微妙的退化现象——出现在无迹字符变体的背景下。

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The correspondence induced on the pillowcase by the earring tangle

The earring tangle consists of four strands $4 pt \times I \subset S^{2} \times I$ and one meridian around one of the strands. Equipping this tangle with a nontrivial $S O (3)$ bundle, we show that its traceless $S U (2)$ flat moduli space is topologically a smooth genus three surface. We also show that the restriction map from this surface to the traceless flat moduli space of the boundary of the earring tangle is a particular Lagrangian immersion into the product of two pillowcases. The latter computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties.

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.