Related papers: A gluing operation for dimer quivers
We study the behavior of a dimer model under the operation of removing a corner from the lattice polygon and taking the convex hull of the rest. This refines an operation of Gulotta, and the special McKay correspondence plays an essential…
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding…
In this article, we introduce the concept of partial actions of a group $G$ on quivers and demonstrate that for any given partial action of G on a quiver $\Gamma$, there exists another quiver, $\Gamma'$ with a full $G$-action. This is an…
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
Recent results by Keller and Nicol{\'a}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other…
Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduce a generalisation of models of algebraic theories to…
The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special…
We associate a quiver to a quasi-triangulation of a non-orientable marked surface and define a notion of quiver mutation that is compatible with quasi-cluster algebra mutation defined by Dupont and Palesi. Moreover, we use our quiver to…
We introduce an associative glueing operation $\oplus_q$ on the space of solutions of the Quantum Yang-Baxter Equations of Hecke type. The corresponding glueing operations for the associated quantum groups and quantum vector spaces are also…
We apply freezing operators to relate different (quantum) upper cluster algebras. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. They also send bases to bases in many…
We decategorify the higher actions on bordered Heegaard Floer strands algebras from recent work of Rouquier and the author and identify the decategorifications with certain actions on exterior powers of homology groups of surfaces. We also…
Derived equivalences for Artin algebras (and almost $\nu$-stable derived equivalences for finite-dimensional algebras) are constructed from Milnor squares of algebras. Particularly, three operations of gluing vertices, unifying arrows and…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
We construct an action of a Lie algebra on the homology groups of moduli spaces of stable sheaves on K3 surfaces under some technical conditions. This is a generalization of Nakajima's construction of sl_2-action on the homology groups. In…
In this paper the number of ways to glue a surface of genus $g$ has been investigated. We've proven formulas for the number of gluings sphere from three polygons and from two bicolored polygons. Moreover, we've given a new proofs on the…
We extend Turaev's theory of Euler structures and torsion invariants on 3-manifolds to the case of vector fields having generic behavior on the boundary. This allows to easily define gluings of Euler structures and to develop a completely…
We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the…
We study the gluing theory of Riemann surfaces using formal algebraic geometry, and give computable relations between the associated parameters for different gluing processes. As its application to the Liouville conformal field theory, we…
We start with a disk with $2n$ vertices along its boundary where pairs of vertices are connected with $n$ strips with certain restrictions. This forms a {\it pairing}. To relate two pairings, we define an operator called a cut-and-glue…