Related papers: Classification of Links Up to 0-Solvability

We classify four-dimensional connected simply-connected indecomposable Lorentzian symmetric spaces $M$ with connected nontrivial isotropy group furnishing solutions of the Einstein-Yang-Mills equations. Those solutions with respect to some…

Working over a field of characteristic zero, we give structure theorems for all grade three licci ideals and their minimal free resolutions. In particular, we completely classify such ideals up to deformation. The descriptions of their…

Let $F_{\omega_1}$ be the countable admissible ordinal equivalence relation defined on ${}^\omega 2$ by $x \ F_{\omega_1} \ y$ if and only if $\omega_1^x = \omega_1^y$. It will be shown that $F_{\omega_1}$ is classifiable by countable…

We provide a framework for studying the interplay between concordance and positive mutation and identify some of the basic structures relating the two. The fundamental result in understanding knot concordance is the structure theorem proved…

A countable semigroup is $\aleph_0$-categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into the $\aleph_0$-categoricity of semigroups. Our main results are a…

That announcement gives the structure of totally reducible linear Lie algebras which are the Lie algebra of the holonomy group of (at least) one torsion-free connection. The result uses the (already known) classi cation of the irreducible…

We study a class $\mathfrak{M}$ of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations. This class includes many finite metacyclic…

We characterize those semilattices that give rise to Boolean spaces on their associated spaces of ultrafilters. The class of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

We show that the Artin representation on concordance classes of string links induces a well-defined epimorphism modulo order n twisted Whitney tower concordance, and that the kernel of this map is generated by band sums of iterated…

We develop new tools to analyze the complexity of the conjugacy equivalence relation $E_\mathsf{lo}(G)$, whenever $G$ is a left-orderable group. Our methods are used to demonstrate non-smoothness of $E_\mathsf{lo}(G)$ for certain groups $G$…

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in…

An equilevel algebra is a subalgebra of the space of smooth functions $f: M \to {\mathbb R}$ distinguished in this space by finitely many linear conditions of the type $f(x_i) = f(\tilde x_i)$, $x_i \neq \tilde x_i \in M$, or approximated…

A conjecture by Corti, Filip and Petracci, inspired by mirror symmetry, states that smoothing types of affine Gorenstein toric 3-folds correspond to zero mutable Laurent polynomials. We propose a method to prove this conjecture via log…

For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S^3, such a sequence of polynomials arises naturally as the orders of certain…

We work in the smooth category. Let $N$ be a closed connected orientable 4-manifold with torsion free $H_1$, where $H_q := H_q(N; \mathbb Z)$. Our main result is a readily calculable classification of embeddings $N\to\mathbb R^7$ up to…

We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators…

This paper explores the structure of low-dimensional cohomology groups in the context of complex nilpotent associative algebras. Specifically, we study 5-dimensional complex nilpotent associative algebras satisfying $\mathcal{A}^4 = 0$ and…

In this paper we introduce the graph $\Gamma_{sc}(G)$ associated with a group $G$, called the solvable conjugacy class graph (abbreviated as SCC-graph), whose vertices are the nontrivial conjugacy classes of $G$ and two distinct conjugacy…

Let $n \geq 2$. We prove a homological stability theorem for the diffeomorphism groups of $(4n+1)$-dimensional manifolds, with respect to forming the connected sum with $(2n-1)$-connected, $(4n+1)$-dimensional manifolds that are stably…