平衡超椭圆映射类群由三个元素生成

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2024-01-24 DOI:10.1515/advgeom-2023-0026

Genki Omori

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引用次数: 0

摘要

平衡超椭圆映射类群是总曲面映射类群中平衡超椭圆覆盖的变换群的归一化。我们证明，具有一个标记点、一个边界分量或无标记点和边界的平衡超椭圆映射类群由三个元素生成。为了证明这一点，我们还证明了其可提升映射类群也由三个元素生成。除了封闭曲面的几种情况外，这些生成集都是最小的。

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The balanced superelliptic mapping class groups are generated by three elements

The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering in the mapping class group of the total surface. We prove that the balanced superelliptic mapping class groups with either one marked point, one boundary component, or no marked points and boundary are generated by three elements. To prove this, we also show that its liftable mapping class groups are also generated by three elements. These generating sets are minimal except for several cases of closed surfaces.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.