Related papers: Homology and Derived Series of Groups II: Dwyer's …

This paper verifies a conjecture of Edelman and Reiner regarding the homology of the $h$-complex of a Boolean algebra. A discrete Morse function with no low-dimensional critical cells is constructed, implying a lower bound on connectivity.…

The notion of acyclic matching property was provided by Losonczy and it was proved that torsion-free groups admit this property. In this paper, we introduce a duality of acyclic matching as a tool for classification of some Abelian groups,…

We prove that Real topological Hochschild homology can be characterized as the norm from the cyclic group of order $2$ to the orthogonal group $O(2)$. From this perspective, we then prove a multiplicative double coset formula for the…

A 2-group is a "categorified" version of a group, in which the underlying set G has been replaced by a category and the multiplication map has been replaced by a functor. Various versions of this notion have already been explored; our goal…

As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to…

Let $\pi\colon P\to M$ be a principal bundle and $p$ an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern-Simons differential characters is exploited to define an homology map $\chi^{k} :…

One way to understand the deformation theory of a tensor category $M$ is through its Davydov-Yetter cohomology $H_{DY}^{\ast}(M)$ which in degree 3 and 4 is known to control respectively first order deformations of the associativity…

We develop a geometric framework that characterizes the synchronization problem --- the problem of consistently registering or aligning a collection of objects. The theory we formulate characterizes the cohomological nature of…

The canonical trace on the reduced C*-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C^*-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the…

Faltings' approach in $p$-adic Hodge theory can be schematically divided into two main steps: firstly, a local reduction of the computation of the $p$-adic \'etale cohomology of a smooth variety over a $p$-adic local field to a Galois…

As is well-known, the homology groups of the complement of a complex hyperplane arrangement are torsion-free. Nevertheless, as we showed in a recent paper [arXiv:1209.3414] the homology groups of the Milnor fiber of such an arrangement can…

Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative…

We compare three definitions of the equivariant cohomological dimension of a group with operators, coming from Takasu, Adamson and Bredon relative group cohomologies, giving examples of strict inequality in all cases where it can occur. We…

The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on…

We introduce two new homology theories of orbifolds from some special type of triangulations adapted to an orbifold, called AW-homology and DW-homology. The main idea in the definitions of these two homology theories is that we use…

We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…

We consider the associated graded $\bigoplus_{k\geq 1} \Gamma_k \mathcal{I} / \Gamma_{k+1} \mathcal{I} $ of the lower central series $\mathcal{I} = \Gamma_1 \mathcal{I} \supset \Gamma_2 \mathcal{I} \supset \Gamma_3 \mathcal{I} \supset…

Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or the \v{C}ech nerve of a good open cover. Upon embedding the…

The homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…