Prym representations of the handlebody group

Bader, P. (2024) Prym representations of the handlebody group. Geometriae Dedicata, 218(3), 59. (doi: 10.1007/s10711-024-00911-5)

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.

• Item Type: Articles
• Additional Information: This work was written while the author was supported by the UKRI Grant (Number: EP/V521917/1).
• Keywords: Representation theory of groups, mapping class groups, handlebody group, twist group.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bader, Mr Philipp
• Authors: Bader, P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Geometriae Dedicata
• Publisher: Springer
• ISSN: 0046-5755
• ISSN (Online): 1572-9168
• Published Online: 29 March 2024
• Copyright Holders: Copyright © 2024 The Authors
• First Published: First published in Geometriae Dedicata 218(3): 59
• Publisher Policy: Reproduced under a Creative Commons License