Related papers: Unlinking symmetric quivers
The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be…
The knots-quivers correspondence is a relation between knot invariants and enumerative invariants of quivers, which in particular translates the knot operations of linking and unlinking to a certain mutation operation on quivers. In this…
The generalized knots-quivers correspondence extends the original knots-quivers correspondence, by allowing higher level generators of quiver generating series. In this paper we explore the underlined combinatorics of such generating…
Given a permutation pattern p and an equivalence relation on permutations, we study the corresponding equivalence classes all of whose members avoid p. Four relations are studied: Conjugacy, order isomorphism, Knuth-equivalence and toric…
Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver…
Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagram of a permutation. We show that the permutations which…
We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish…
We prove that the extended Khovanov arc algebras are isomorphic to the basic algebras of anti-spherical Hecke categories for maximal parabolics of symmetric groups. We present these algebras by quiver and relations and provide the full…
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implications for realizing all knots and links as special types of…
In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of the descent algebra as a homomorphic image…
We consider a quiver structure on the set of quandle colorings of an oriented knot or link diagram. This structure contains a wealth of knot and link invariants and provides a categorification of the quandle counting invariant in the most…
We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-PT skein relations, we confirm the stable growth of…
Cut-diagrams are diagrammatic objects, defined in dimensions 1 and 2, that generalize links in 3-space and surface-links in 4-space; in dimension 1, this coincides with the theory of welded links. Using cut-diagrams, we introduce an…
We introduce and explore the relation between knot invariants and quiver representation theory, which follows from the identification of quiver quantum mechanics in D-brane systems representing knots. We identify various structural…
We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the…
In this paper we analyze symmetries, hidden symmetries, and commensurability classes of $(\epsilon, d_L)$-twisted knot complements, which are the complements of knots that have a sufficiently large number of twists in each of their twist…
We determine the algebraic structure underlying the geometric complex associated to a link in Bar-Natan's geometric formalism of Khovanov's link homology theory (n=2). We find an isomorphism of complexes which reduces the complex to one in…
We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some…
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…
We construct the complete invariant for fused links. It is proved that the set of equivalence classes of $n$-component fused links is in one-to-one correspondence with the set of elements of the abelization $UVP_n/UVP_n^{\prime}$ up to…