Related papers: A conjecture on superconnected quandles

We study the structure of finite quandles in terms of subquandles. Every finite quandle $Q$ decomposes in a natural way as a union of disjoint $Q$-complemented subquandles; this decomposition coincides with the usual orbit decomposition of…

Quandles can be regarded as generalizations of symmetric spaces. In the study of symmetric spaces, the notion of flatness plays an important role. In this paper, we define the notion of flat quandles, by referring to the theory of…

We prove that an Alexander quandle of prime order is generated by any pair of distinct elements. Furthermore, we prove for such a quandle that any ordered pair of distinct elements can be sent to any other such pair by an automorphism of…

We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we…

This article surveys many aspects of the theory of quandles which algebraically encode the Reidemeister moves. In addition to knot theory, quandles have found applications in other areas which are only mentioned in passing here. The main…

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

A quandle is an algebraic structure whose axioms correspond to the Reidemeister moves of knot theory. S. Kamada introduced the notion of a quandle with a good involution, which is later called a symmetric quandle. We are interested in the…

We give a description of the construction of Chevalley supergroups, providing some explanatory examples. We avoid the discussion of the $A(1,1)$, $P(3)$ and $Q(n)$ cases, for which our construction holds, but the exposition becomes more…

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.

Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby identify and discover 'types': of behaviour, views,…

We explain how the medial quandle of a classical or virtual link can be built from the peripheral structure of the reduced Alexander module.

In this paper, we give a characterization of homogeneous quandles with abelian inner automorphism groups. In particular, we show that such a quandle is expressed as an abelian extension of a trivial quandle. Our construction is a…

We formulate a conjecture on local geometric Langlands for supercuspidal representations using Yu's data and Feigin-Frenkel isomorphism. We refine our conjecture for a large family of regular supercuspidal representations defined by…

We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…

We propose a method to efficiently construct data-dependent kernels which can make use of large quantities of (unlabeled) data. Our construction makes an approximation in the standard construction of semi-supervised kernels in Sindhwani et…

This paper has partially a novel and partially a survey character. We start with a short review of rack (two term) homology of self distributive algebraic structures (shelves) and their connections to knot theory. We concentrate on a…

We provide a quantum model for the recent experiment coupling a tardigrade to superconducting qubits. A number of different perspectives are discussed with the emphasis placed on quantum entanglement between different subsystems involved in…

A quandle is an algebra with two binary operations satisfying three conditions which are related to Reidemeister moves in knot theory. In this paper we introduce the notion of the (canonical) tensor product of a quandle. The tensor product…

By using superisolated surface singularities whose link is a rational homology sphere we give counterexamples to some of the most important conjetures concernig invariants of normal surface singularities.