Related papers: On the algorithmic construction of classifying spa…

A group $\Gamma$ is defined to be cofinitely Hopfian if every homomorphism $\Gamma\to\Gamma$ whose image is of finite index is an automorphism. Geometrically significant groups enjoying this property include certain relatively hyperbolic…

Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$…

In this paper we introduce a homotopy theoretic technique for proving that the $K$-theoretic assembly map is an equivalence. It is an extension of the methods used to prove split injectivity of the assembly and applies to any geometrically…

Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the…

A group $\Gamma$ has separable cohomology if the profinite completion map $\iota \colon \Gamma \to \widehat{\Gamma}$ induces an isomorphism on cohomology with finite coefficient modules. In this article, cohomological separability is…

The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the…

Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to…

We address the question of determining which mapping class groups of infinite-type surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let $\Sigma$ be a connected, orientable surface of infinite type with…

We study cocycles of countable groups $\Gamma$ of Borel automorphisms of a standard Borel space $(X, \mathcal{B})$ taking values in a locally compact second countable group $G$. We prove that for a hyperfinite group $\Gamma$ the subgroup of…

We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…

We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of hyperbolic group on a…

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

The paper examines machines of the type of the $\Gamma$-spaces of Segal which describe homotopy structures on topological spaces. The main result of the paper shows that for any such machine one can find an algebraic theory characterizing…

The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) embeds into a nonstandard free group with hyperfinitely many…

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of…

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

We exhibit examples of finitely presented subgroups $P$ of direct products of hyperbolic groups for which there is no algorithm that detects whether a finitely presented group has a quotient isomorphic to $P$. For any torsion-free, linear,…

We construct a polynomial-time algorithm which given a graph $\Gamma$ finds the full set of non-equivalent Cayley representations of $\Gamma$ over the group $D\cong C_p\times C_{p^k}$, where $p\in\{2,3\}$ and $k\geq 1$. This result implies…