6 papers
6-valent vertex in the web category and its categorification
Jernej Grlj, Mikhail Khovanov, Haihan Wu +1
We define a -rotationally invariant 6-valent vertex in the web category. When , we provide a categorification of the 6-valent vertex using $\mathf…
Pairs of eventually constant maps and nilpotent pairs
Weixi Chen, Mee Seong Im, Mikhail Khovanov +2
Tom Leinster gave a bijective correspondence between the set of operators on a finite-dimensional vector space and the set of pairs consisting of a nilpotent operator and a vec…
Annular SL(2) and SL(3) web algebras
Rostislav Akhmechet, Mikhail Khovanov, Melissa Zhang
We use annular foam TQFTs introduced by the first two authors to define equivariant and web algebras in the annulus. To a diagram of a tangle in the thickened annul…
Lectures on SL(3) foams and link homology
Mikhail Khovanov, Dmitry Solovyev
These notes are based on the three lectures that one of the authors gave at Tsinghua University in the summer of 2023 as part of the workshop on Geometric Representation Theory and…
Two-dimensional topological quantum field theories of rank two over Dedekind domains
Fabian Espinoza, Mee Seong Im, Mikhail Khovanov
We give examples of Frobenius algebras of rank two over ground Dedekind rings which are projective but not free and discuss possible applications of these algebras to link homology…
Entropy, cocycles, and their diagrammatics
Mee Seong Im, Mikhail Khovanov
The first part of the paper explains how to encode a one-cocycle and a two-cocycle on a group with values in its representation by networks of planar trivalent graphs with edge…