Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 019, 32 pages      arXiv:1911.02503      https://doi.org/10.3842/SIGMA.2020.019
Contribution to the Special Issue on Algebra, Topology, and Dynamics in Interaction in honor of Dmitry Fuchs

A Faithful Braid Group Action on the Stable Category of Tricomplexes

Mikhail Khovanov a and You Qi b
a)  Department of Mathematics, Columbia University, New York, NY 10027, USA
b)  Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA

Received November 07, 2019, in final form March 19, 2020; Published online March 29, 2020

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.

Key words: braid group; categorical action; bicomplexes; spectral sequence; tricomplexes; stable category.

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