Related papers: Central extensions and the classifying spaces of p…

In this paper we describe a classifying theory for families of simplicial topological groups. If $B$ is a topological space and $G$ is a simplicial topological group, then we can consider the non-abelian cohomology $H(B,G)$ of $B$ with…

We classify extensions of a group $G$ by a braided 2-group $\mathcal{B}$ as defined by Drinfeld, Gelaki, Nikshych, and Ostrik. We describe such extensions as homotopy classes of maps from the classifying space of $G$ to the classifying…

We discuss two aspects of the presentation of the theory of principal infinity-bundles in an infinity-topos, introduced in [NSSa], in terms of categories of simplicial (pre)sheaves. First we show that over a cohesive site C and for G a…

Finite $p$-groups of nilpotency class 2 are treated from the perspective of central extensions. Given finite abelian groups $G,A$, we derive an explicit formula for cocycles representing elements of $H^2(G,A)$, compute $H^2(G,A)$, and…

Let $G$ be a finite group having a factorisation $G=AB$ into subgroups $A$ and $B$ with $B$ cyclic and $A\cap B=1,$ and let $b$ be a generator of $B$. The associated skew-morphism is the bijective mapping $f:A \to A$ well defined by the…

In the present paper we study abelian extensions of connected Lie groups $G$ modeled on locally convex spaces by smooth $G$-modules $A$. We parametrize the extension classes by a suitable cohomology group $H^2_s(G,A)$ defined by locally…

Gerbes are locally connected presheaves of groupoids. They are classified up to local weak equivalence by path components in a 2-cocycle category taking values in all sheaves of groups, their isomorphisms and homotopies. If F is a full…

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

We prove that the category of preordered groups contains two full reflective subcategories that give rise to some interesting Galois theories. The first one is the category of the so-called commutative objects, which are precisely the…

We determine a subring of the Chow ring and the cohomology of $BPGL_n$, the classifying space of the projective linear group of degree $n$ over complex numbers, and explain a way in which this computation might play a role in the…

We prove the graded braided commutativity of the Hochschild cohomology of $A$ with trivial coefficients, where $A$ is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some…

We show that every nilpotent group of class at most two may be embedded in a central extension of abelian groups with bilinear cocycle. The embedding is shown to depend only on the base group. Some refinements are obtained by considering…

Let G be an infinitesimal group scheme of finite height r and V(G) the scheme which represents 1-parameter subgroups of G. We consider sheaves over the projectivization P(G) of V(G) constructed from a G-module M. We show that if P(G) is…

Let p, ell be distinct primes and let q be a power of p. Let G be a connected compact Lie group. We show that there exists an integer b such that the mod ell cohomology of the classifying space of a finite Chevalley group G(F_q) is…

This paper is devoted to the study of the gluing construction for perverse sheaves on $G/U$ introduced by Kazhdan and Laumon ($G$ is a semisimple gourp, $U$ is the unipotent radical of a Borel subgroup in $G$). Kazhdan and Laumon…

We give a geometric model for the category of coherent sheaves over the weighted projective line of type $(p,q)$ in terms of an annulus with marked points on its boundary. We establish a bijection between indecomposable sheaves over the…

A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra B. We prove that principality…

In this paper, we classify conjugacy classes of centralizers of irreducible subgroups in $PSL(n,\mathbb{C})$ using alternate modules a.k.a. finite abelian groups with an alternate bilinear form. When $n$ is squarefree, we prove that these…

Henn, Lannes, and Schwartz have introduced two invariants, d_0(G) and d_1(G), of the mod p cohomology of a finite group G such that H^*(G) is detected and determined by H^d(C_G(V)) for d no bigger than d_0(G) and d_1(G), with V < G…

If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X).…