Related papers: Conley: Computing connection matrices in Maple
We develop an algorithm for computing generalized Seifert matrices for colored links given as closures of colored braids. The algorithm has been implemented by the second author as a computer program called Clasper. Clasper also outputs the…
We use product systems of $C^*$-correspondences to introduce twisted $C^*$-algebras of topological higher-rank graphs. We define the notion of a continuous $\mathbb{T}$-valued $2$-cocycle on a topological higher-rank graph, and present…
We interpret mathematically the pair (master equation, solution of master equation) up to equivalence, as the pair (a presentation of a free triangular dga T over a combination operad O, dga map of T into C, a dga over O) up to homotopy…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some…
Graph data management and querying has many practical applications. When graphs are very heterogeneous and/or users are unfamiliar with their structure, they may need to find how two or more groups of nodes are connected in a graph, even…
We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\times G$ by the so-called gauge…
This note is devoted to a trick which yields almost trivial proofs that certain complexes associated to topological surfaces are connected or simply connected. Applications include new proofs that the complexes of curves, separating curves,…
We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…
We construct a representation of the braid groups in a cluster C*-algebra coming from a triangulation of the Riemann surface S with one or two cusps. It is shown that the Laurent polynomials attached to the K-theory of such an algebra are…
We offer a Maple package {\tt Poincare\_Series} for calculating the Poincar\'e series for the algebras of invariants/covariants of binary forms, for the algebras of joint invariants/covariants of several binary forms, for the kernel of…
We begin by reviewing the definition of 3-Lie algebras and the fundamental concepts of matched pairs. Subsequently, we introduce the representation theory of matched pairs and define the semidirect product. Building on this foundation, we…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
We find a new braided Hopf structure for the algebra satisfied by the entries of the braided matrix $BSL_q(2)$. A new nonbraided algebra whose coalgebra structure is the same as the braided one is found to be a two parameter deformed…
The notion of holonomy $R$-matrices is introduced. It is shown how to define invariants of tangles with flat connections in a principle $G$-bundle of the complement of a tangle using holonomy $R$-matrices.
We define a notion of a connectivity structure on an $\infty$-category, analogous to a $t$-structure but applicable in unstable contexts -- such as spaces, or algebras over an operad. This allows us to generalize notions of n-skeleta,…
Homological algebra is often understood as the translator between the world of topology and algebra. However, this branch of mathematics is worth studying by itself, given that it provides fascinating perspectives about other disciplines,…
There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…