A faithful braid group action on the stable category of tricomplexes

TL;DR

This paper introduces a new faithful categorical braid group action on the stable category of tricomplexes, expanding the understanding of complex algebraic structures in geometry and algebra.

Contribution

It presents a novel faithful braid group action on the stable category of tricomplexes, offering new insights into their categorical and algebraic properties.

Findings

Reinterpreted spectral sequence arrows via indecomposable summands.

Established a faithful braid group action on tricomplexes.

Enhanced understanding of algebraic structures in geometry.

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 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.