Related papers: On Core Quandles

We review the definition of a quandle, and in particular of the core quandle $\mathrm{Core}(G)$ of a group $G$, which consists of the underlying set of $G$, with the binary operation $x\lhd y = x y^{-1} x$. This is an involutory quandle,…

We obtain the codegree of a certain primitive character for a finite solvable group, and thereby give a negative answer to a question proposed by Moret\'o in \cite{Moreto}.

Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…

Neuronal circuits of the cerebral cortex are the structural basis of mammalian cognition. The same qualitative components and connectivity motifs are repeated across functionally specialized cortical areas and mammalian species, suggesting…

We prove a homological characterization of $Q$-manifolds bundles over $C$-spaces. This provides a partial answer to Question QM22 from \cite{w}.

Here we analyze a proper 2-generated core in a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank. We ultimately show that such a group is strongly embedded and the ambiant group is…

The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandle cohomology and certain group of automorphisms of an…

We define a class of quandle-like structures called pseudoquandles and analyze some of their algebraic properties.

In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a…

Cox rings of normal varieties are factorially graded, i.e. homogeneous elements allow a unique decomposition into homogeneous factors. We study this property from an algebraic point of view and give a criterion which in a sense reduces it…

This document specifies a core version of the type theory implemented in the Cedille tool. Cedille is a language for dependently typed programming and computer-checked proof. Cedille can elaborate source programs down to Cedille Core, which…

We investigate a few aspects of the notion of Levi core, introduced by the authors in a previous work: a basic finiteness question, the connections with Kohn's algorithm and with Catlin's property (P).

Let U be an open subset of a unirational variety (or more generally of a separably rationally connected variety). We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U.…

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely…

Given a quandle, we can construct a symmetric quandle called the symmetric double of the quandle. We show that the (co)homology groups of a given quandle are isomorphic to those of its symmetric double. Moreover, quandle coloring numbers…

Complex networks can be used to represent complex systems which originate in the real world. Here we study a transformation of these complex networks into simplicial complexes, where cliques represent the simplices of the complex. We extend…

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…

This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. The proof first translates Handa's characterization of…

In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind…

We propose various problems about Borel complexity of characterized subgroups of compact abelian groups, inspired by our forthcoming paper \cite{DI3}.