Prym representations of the handlebody group

Pub Date : 2024-03-29 DOI:10.1007/s10711-024-00911-5

引用次数: 0

Abstract

Let S be an oriented, closed surface of genus g. The mapping class group of S is the group of orientation preserving homeomorphisms of S modulo isotopy. In 1997, Looijenga introduced the Prym representations, which are virtual representations of the mapping class group that depend on a finite, abelian group. Let V be a genus g handlebody with boundary S. The handlebody group is the subgroup of those mapping classes of S that extend over V. The twist group is the subgroup of the handlebody group generated by twists about meridians. Here, we restrict the Prym representations to the handlebody group and further to the twist group. We determine the image of the representations in the cyclic case.

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手柄体群的普赖姆表征

S 的映射类群是 S 的方向保持同构群。1997 年，Looijenga 引入了 Prym 表示，它是映射类群的虚拟表示，取决于一个有限的无性群。让 V 是具有边界 S 的 g 属手柄体。手柄体群是 S 的映射类在 V 上延伸的子群。在此，我们将 Prym 表示限定于柄体群，并进一步限定于扭转群。我们将确定循环情况下的表示的图像。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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