Branched Cauchy–Riemann structures on once-punctured torus bundles

IF 0.5 4区 数学 Q3 MATHEMATICS
Alex Casella
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引用次数: 0

Abstract

Unlike in hyperbolic geometry, the monodromy ideal triangulation of a hyperbolic once-punctured torus bundle $M_f$ has no natural geometric realization in Cauchy–Riemann (CR) space. By introducing a new type of 3‑cell, we construct a different cell decomposition $\mathcal{D}_f$ of $M_f$ that is always realisable in CR space. As a consequence, we show that every hyperbolic once-punctured torus bundle admits a branched CR structure, whose branch locus is contained in the union of all edges of $\mathcal{D}_f$. Furthermore, we explicitly compute the ramification order around each component of the branch locus and analyse the corresponding holonomy representations.
一次穿刺环束上的分支柯西-黎曼结构
与双曲几何不同,双曲一次穿刺环面束的单理想三角剖分在Cauchy-Riemann (CR)空间中没有自然的几何实现。通过引入一种新的3 - cell,我们构造了一个不同的cell分解$\mathcal{D}_f$,该分解$M_f$在CR空间中总是可实现的。因此,我们证明了每一个双曲一次穿孔环面束都存在一个分支的CR结构,其分支轨迹包含在$\mathcal{D}_f$的所有边的并中。此外,我们显式地计算了分支轨迹各分量周围的分支顺序,并分析了相应的完整表示。
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes original research papers and survey articles on all areas of pure mathematics and theoretical applied mathematics.
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