Related papers: Axis bundles in free-by-cyclic groups

In this short review article we sketch some developments which should ultimately lead to the analogy of the Chern-Weil homomorphism for principal bundles in the realm of non-commutative differential geometry. Principal bundles there should…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

The notion of fractional monodromy was introduced by Nekhoroshev, Sadovski\'{i} and Zhilinski\'{i} as a generalization of standard (`integer') monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of…

In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is well-understood. Here we consider the question for non-free…

A group is boundedly acyclic if its bounded cohomology with trivial real coefficients vanishes in all positive degrees. Amenable groups are boundedly acyclic, while the first non-amenable examples were the group of compactly supported…

In this paper we prove that a fully irreducible outer automorphism relative to a non-exceptional free factor system acts loxodromically on the relative free factor complex as defined by Handel and Mosher. We also prove a north-south dynamic…

We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…

We prove similar theorems concerning the structure of bundles involving complements of fiber-type hyperplane arrangements and orbit configuration spaces. These results facilitate analysis of the fundamental groups of these spaces, which may…

Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $\chi(M)\ne 0$. We show that if $G$ is a finite group of 2-rank $\le 1$ which admits a homologically…

The positive cohomology groups of a finite group acting on a ring vanish when the ring has a norm-one element. In this note we give explicit homotopies on the level of cochains when the group is cyclic, which allows us to express any…

We compute the mapping class group-valued monodromy of any sufficiently ample linear system on any smooth simply connected projective surface, identifying this with the r-spin mapping class group associated to a maximal root of the adjoint…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

It was proved that for any finite set of elements of a free product of residually finite groups such that no two of them belong to conjugate cyclic subgroups and each of them do not belong to a subgroup which is conjugate a to free factor…

We consider the existence of bibundles, in other words locally trivial principal $G$ spaces with commuting left and right $G$ actions. We show that their existence is closely related to the structure of the group $\Out(G)$ of outer…

The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandle cohomology and certain group of automorphisms of an…

We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among FINITE graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the…

Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only if $A$ is representation finite and simply…