A Faithful Braid Group Action on the Stable Category of Tricomplexes

Abstract

Bicomplexes of vector spaces frequently appear throughout algebra and geometry. In Section 2, we explain how to think about the arrows in the spectral sequence of a bicomplex via its indecomposable summands. Polycomplexes seem to be much rarer. In Section 3 of this paper, we rethink a well-known faithful categorical braid group action via an action on the stable category of tricomplexes.