Generalized Long-Moody functors

Soulie, A. (2022) Generalized Long-Moody functors. Algebraic and Geometric Topology, 22(4), pp. 1713-1788. (doi: 10.2140/agt.2022.22.1713)

Abstract

We generalize the principle of the Long–Moody construction for representations of braid groups to other groups, such as mapping class groups of surfaces. Namely, we introduce endofunctors over a functor category that encodes representations of a family of groups. They are called Long–Moody functors and provide new representations. In this context, notions of polynomial functors are defined and play an important role in the study of homological stability. We prove that, under additional assumptions, a Long–Moody functor increases the very strong and weak polynomial degrees of functors by one.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Soulie, Dr Arthur
• Authors: Soulie, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Algebraic and Geometric Topology
• Publisher: Mathematical Sciences Publishers
• ISSN: 1472-2747
• ISSN (Online): 1472-2739
• Copyright Holders: Copyright © 2022 Mathematical Sciences Publishers
• First Published: First published in Algebraic and Geometric Topology 22(4):1713-1788
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher