Related papers: Edge contraction on dual ribbon graphs and 2D TQFT

We study the superconformal indices of 4d theories coming from 6d N=(2,0) theory of type \Gamma on a Riemann surface, with the action of the outer-automorphism \sigma in the trace. We find that the indices are given by the partition…

We construct and study a new family of TQFTs based on nilpotent highest weight representations of quantum sl(2) at a root of unity indexed by generic complex numbers. This extends to cobordisms the non-semi-simple invariants defined in…

We investigate the structure of two-dimensional partial cubes, i.e., of isometric subgraphs of hypercubes whose vertex set defines a set family of VC-dimension at most 2. Equivalently, those are the partial cubes which are not contractible…

For a commutative Frobenius algebra $A$, we construct a $(2,3,3+\varepsilon)$-dimensional TQFT $\mathsf{AFK}_A$ that assigns to a 3-manifold a skein module of embedded $A$-decorated surfaces. These surface skein modules have been first…

We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few…

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary,…

We develop filtered-graded techniques for algebras in monoidal categories with the main goal of establishing a categorical version of Bongale's 1967 result: A filtered deformation of a Frobenius algebra over a field is Frobenius as well.…

In this paper, we describe a relation between a categorical quantization construction, called "2-linearization", and extended topological quantum field theory (ETQFT). We then describe an extension of the 2-linearization process which…

We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell…

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of…

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion…

We study the behaviors of cohomological Hall algebras and relevant subjects under an edge contraction. Given a quiver with potential and fix an arrow, the edge contraction is a way to construct a new quiver with potential. We show that…

We endow twisted tensor products with a natural notion of counit and comultiplication, and we provide sufficient and necessary conditions making the twisted tensor product a counital coassociative coalgebra. We then characterize when the…

The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant topological field theories (TFT2), by using a vertex operator formalism for the…

For any symmetric monoidal category $\mathcal{D}$, Lauda and Pfeiffer showed the equivalence between the $\mathcal{D}$-valued open-closed 2-dimensional TQFTs and the so-called knowledgeable Frobenius algebras (KFAs) in $\mathcal{D}$. Each…

We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex $Q^-_3$ (here contraction means contracting the edges…

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT).…

We show that Caratheodory's conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one umbilic in the graphs of functions f: R^2-->R whose gradient decays uniformly faster than…

To each finitely aligned higher-rank graph $\Lambda$ and each $\mathbb{T}$-valued 2-cocycle on $\Lambda$, we associate a family of twisted relative Cuntz-Krieger algebras. We show that each of these algebras carries a gauge action, and…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…