A Faithful Braid Group Action on the Stable Category of Tricomplexes

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 more rare.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.