Abstract The Temperley–Lieb algebra is a fundamental component of SU (2) topological
quantum field theories. We construct chain complexes corresponding to minimal …

We show that the Khovanov complex of a connected link diagram D retracts to a subcomplex
whose generators are in 2: 1 correspondence with the spanning trees of the" black graph" of …

We define a wall-crossing morphism for Khovanov-Rozansky homology; that is, a map
between the KR homology of knots related by a crossing change. Using this map, we extend …

Quantum topology began in the 1980s with the Jones polynomial [29] and Witten's
reinterpretation of it via Yang–Mills theory [59]. Witten's work was at a physical level of rigor …

This paper begins with a survey of some applications of Khovanov homology to low-
dimensional topology, with an eye toward extending these results to 𝔰 𝔩 (n) homologies. We …

We show that over the binary field 𝔽 2, the Bar-Natan perturbation of Khovanov homology
splits as the direct sum of its two reduced theories, which we also prove are isomorphic. This …

This paper is an introduction to Khovanov homology. We start with a quick introduction to the
bracket polynomial, reformulating it and the Jones polynomial so that the value of an …

An algorithmic method of finding combinatorial formulas for knot invariants and other
cohomology classes of spaces of knots in Rn, n≥ 3, is described. In the case of invariants of …

Inspired by bordered Floer homology, we describe a type A structure in Khovanov
homology, which complements the type D structure previously defined by the author. The …