Related papers: Injectivity theorems and algebraic closures of gro…

We construct an embedding G of the category of graphs into the category of abelian groups such that for graphs X and Y we have Hom(GX,GY)=Z[Hom(X,Y)], the free abelian group whose basis is the set Hom(X,Y). The isomorphism is functorial in…

We prove that virtually torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property, a notion recently introduced by Ab\'ert, Bergeron, Fr\k{a}czyk and Gaboriau. As a consequence, the…

We observe that the results of Feighn-Handel and Geoghegan-Mihalik-Sapir-Wise about coherence and Hopficity of mapping tori of injective endomorphisms of free groups extend to non-injective endomorphisms.

We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that…

We prove that $F$-injectivity localizes, descends under faithfully flat homomorphisms, and ascends under flat homomorphisms with Cohen-Macaulay and geometrically $F$-injective fibers, all for arbitrary Noetherian rings of prime…

We show that the well-known fact that the equivariant cohomology of a torus action is a torsion-free module if and only if the map induced by the inclusion of the fixed point set is injective generalises to actions of arbitrary compact…

I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…

Gersten's injectivity conjecture for a functor $F$ of ``motivic type'', predicts that given a semilocal, ``non-singular'', integral domain $R$ with a fraction field $K$, the restriction morphism induces an injection of $F(R)$ inside $F(K)$.…

We give new information about the relationship between the low-dimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group.…

The embedding theorem of Roelcke and Dierolf for the completions of four standard uniform structures on topological groups and their quotients holds more generally for spaces of uniform measures. The natural mappings between the four spaces…

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…

Let K be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. Assuming that S is a closed, orientable surface of genus at least 4, we confirm a conjecture of Farb that Comm(K), Aut(K)…

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

Starting from context-free inverse graphs, we introduce a new class of groups and study their structural properties. We establish closure properties, show that their co-word problems are context-free, analyze torsion elements, and realize…

Using algebraic and topological K-theory together with complex C^*-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and…

In this article, we give a generalization to injective modules by using $e$-exact sequences introduced by Akray in [1] and name it $e$-injective modules and investigate their properties. We reprove both Baer criterion and comparison theorem…

For a natural class of cohomology theories with support (including \'etale or pro-\'etale cohomology with suitable coefficients), we prove a moving lemma for cohomology classes with support on smooth quasi-projective k-varieties that admit…

We define a class $\mathcal{U}$ of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely generated. Assume that $G$ is a group in $\mathcal{U}$ and…

We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an \'etale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X.…

The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet)…