Related papers: On CW-complexes over groups with periodic cohomolo…

In this paper we consider classifying spaces of a family of $p$-groups and we prove that mod $p$ cohomology enriched with Bockstein spectral sequences determines their homotopy type among $p$-completed CW-complexes. We end with some…

In 2011, Guralnick and Tiep proved that if $G$ was a Chevalley group with Borel subgroup $B$ and $V$ an irreducible $G$-module in cross characteristic with $V^B = 0$, then the the dimension of $H^1(G,V)$ is determined by the structure of…

A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields.…

For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\in\Bbb N$, there exists a 1-connected rational CW-complex…

Let $p:X \rightarrow S$ be a flat, proper and regular scheme over a strictly henselian discrete valuation ring. We prove that the singularity category of the special fiber with its natural two-periodic structure allows to recover the…

Hodge classes on the moduli space of admissible covers with monodromy group G are associated to irreducible representations of G. We evaluate all linear Hodge integrals over moduli spaces of admissible covers with abelian monodromy in terms…

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…

We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincar\'e polynomial. We prove a Terao-type factorization statement on the splitting of…

It is one of the wonderful ``coincidences'' of the theory of finite groups that the simple group G of order 25920 arises as both a symplectic group in characteristic 3 and a unitary group in characteristic 2. These two realizations of G…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having…

The classification problem for principal fibre bundles over two-dimensional CW-complexes is considered. Using the Postnikov factorization for the base space of a universal bundle a Puppe sequence that gives an implicit solution for the…

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…

We apply discrete algebraic Morse theory to calculate the Anick resolution of the group algebra of the group $G_3^2$. As a corollary, we evaluate Hochschild cohomologies of $G_3^2$ with coefficients in all 1-dimensional bimodules. Almost…

Given a finite connected 3-complex with cohomological dimension 2, we show it may be constructed up to homotopy by applying the Quillen plus construction to the Cayley complex of a finite group presentation. This reduces the D(2) problem to…

For $G$ a finite group, one way to construct irreducible quandle representations over $\mathbb{C}$ of the conjugacy quandle $Conj(G)$ is by taking the product of an irreducible linear group representation of $G$ by what we call a quandle…

We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we apply our methods to invariant curves whose branches are…

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for…

Turaev conjectured that the classification, realization and splitting results for Poincar\'e duality complexes of dimension $3$ (PD$_{3}$-complexes) generalize to PD$_{n}$-complexes with $(n-2)$-connected universal cover for $n \ge 3$.…

We treat two quite different problems related to changes of complex structures on K\"ahler manifolds by using global geometric method. First, by using operators from Hodge theory on compact K\"ahler manifold, we present a closed explicit…