Related papers: Transformation groups of certain flat affine manif…

We consider certain groups of tree automorphisms as so-called diffeological groups. The notion of diffeology, due to Souriau, allows to endow non-manifold topological spaces, such as regular trees that we look at, with a kind of a…

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

Affine manifolds are called integral if there is an atlas such that all transition maps are affine transformations with integer matrices of linear parts. In this paper we describe all complete integral affine structures on compact…

We consider log deformations of affine surfaces with fibrations by the affine lines. Such a fibration is of affine type (resp. of complete type) if the base curve of the fibration is an affine curve (resp. a complete curve). The case of…

In this article we consider diffeomorphism groups of manifolds with smooth boundary. We show that the diffeomorphism groups of the manifold and its boundary fit into a short exact sequence which admits local sections. In other words, they…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…

It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the \'etale fundamental groups, then the induced map of the stratified fundamental groups…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its…

Let $f\colon M\to N$ be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that $N$ is not a closed graph-manifold. Suppose that $f$ induces an epimorphism on fundamental groups. We…

We classify compact manifolds of dimension three equipped with a path structure and a fixed contact form (which we refer to as a strict path structure) under the hypothesis that their automorphism group is non-compact. We use a Cartan…

It is proven that the identity component of the group preserving the leaves of a generalized foliation is perfect. This shows that a well-known simplicity theorem on the diffeomorphism group extends to the nontransitive case.

In this paper we characterize permutation groups that are automorphism groups of coloured graphs and digraphs and are abelian as abstract groups. This is done in terms of basic permutation group properties. Using Schur's classical…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

We study manifolds endowed with an (almost) even Clifford (hermitian) structure and admitting a large automorphism group. We classify them when they are simply connected and the dimension of the automorphism group is maximal, and also prove…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…

This is a summary of some of the basic facts about flat 2-orbifold groups, otherwise known as 2-dimensional crystallographic groups. We relate the geometric and topological presentations of these groups, and consider structures…

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of…