Related papers: Effective model of a finite group action

Let $\Gamma_g$ denote the orientation-preserving Mapping Class Group of the genus $g\geq 1$ closed orientable surface. In this paper we show that for fixed $g$, every finite group occurs as a quotient of a finite index subgroup of…

Let G be a finite group acting tamely on a proper reduced curve C over an algebraically closed field. We study the G-module structure on the cohomology groups of a G-equivariant locally free sheaf F on C, and give formulas of…

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, assume that $G$ has a maximal $A$-invariant subgroup $M$ that is a direct product of some isomorphic simple groups, we prove that if $G$ has a…

In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed…

Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in particular by smooth toric varieties and…

For any group $G$ of self homotopy equivalences of the finite nilpotent complex $X$, acting nilpotently on its homology, and for any nilpotent subcomplex $A$, we prove that the universal fibration $$ X \longrightarrow B(*,{\rm…

We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained in the sphere. This is achieved by introducing a type of group presentation…

We study the groups $G$ with the curious property that there exists an element $k\in G$ and a function $f\colon G\to G$ such that $f(xk)=xf(x)$ holds for all $x\in G$. This property arose from the study of near-rings and input-output…

We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i),…

Fix a non-negative integer g and a positive integer I dividing 2g-2. For any Henselian, discretely valued field K whose residue field is perfect and admits a degree I cyclic extension, we construct a curve C over K of genus g and index I.…

We prove a number of results linking properties of actions by compact groups (both quantum and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and extensibility of the actions across several constructions.…

An \textit{algebraic} action of a discrete group $\Gamma $ is a homomorphism from $\Gamma $ to the group of continuous automorphisms of a compact abelian group $X$. By duality, such an action of $\Gamma $ is determined by a module…

Let $(X,x)$ be a pointed geometrically connected smooth projective variety over a sub-$p$-adic field $K$. For any given rank $n$, we prove that there are only finitely many isomorphism classes of representations…

Given a set $X$, the group $\mathrm{Sym}(X)$ consists of all bijections from $X$ to $X$, and $\mathrm{FSym}(X)$ is the subgroup of maps with finite support i.e. those that move only finitely many points in $X$. We describe the automorphism…

The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, this gives rise to a classification of all finite-dimensional…

Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. We…

In the context of almost complex quantization, a natural generalization of algebro-geometric linear series on a compact symplectic manifold has been proposed. Here we suppose given a compatible action of a finite group and consider the…

A finitely presented 1-ended group $G$ has {\it semistable fundamental group at infinity} if $G$ acts geometrically on a simply connected and locally compact ANR $Y$ having the property that any two proper rays in $Y$ are properly…

Let $R$ be a commutative ring and $\Gamma$ be an infinite discrete group. The algebraic $K$-theory of the group ring $R[\Gamma]$ is an important object of computation in geometric topology and number theory. When the group ring is…

Let k be an algebraically closed field of positive characteristic, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG of infinite tame representation type. We find all finitely…