Generalized Long-Moody functors

Abstract

In this paper, 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.

arXiv commentAlgebraic & Geometric Topology, In press

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Cited by in corpus (4)

• Polynomiality of surface braid and mapping class group representations
• Stable twisted cohomology of the mapping class groups in the exterior powers of the unit tangent bundle homology
• Stable twisted cohomology of the mapping class groups in the unit tangent bundle homology
• The Long--Moody construction and twisted Alexander invariants