The cube and the Burnside category
Tyler Lawson, Robert Lipshitz, Sucharit Sarkar
TL;DR
This paper introduces a combinatorial link invariant related to stable homotopy refinements of Khovanov homology, formulated as a functor between 2-categories, and explores its properties.
Contribution
It presents a new combinatorial invariant and develops the theory of functors between 2-categories in the context of link invariants.
Findings
Defines a combinatorial link invariant linked to stable homotopy Khovanov homology.
Establishes properties of functors between 2-categories.
Connects the invariant to recent homotopy refinements of link homology.
Abstract
In this note we present a combinatorial link invariant that underlies some recent stable homotopy refinements of Khovanov homology of links. The invariant takes the form of a functor between two combinatorial 2-categories, modulo a notion of stable equivalence. We also develop some general properties of such functors.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis