Related papers: Groupes de Cremona, connexit\'e et simplicit\'e

Let $\Gamma$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\Gamma$ on the circle is either trivial or semi-conjugate to a unique minimal action on the so-called simple circle.

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

We describe the full group of isometries of each left invariant Riemannian metric on the simply connected unimodular nilpotent or solvable $(R)$-type Lie groups of dimension four.

In this article we classify expanding homogeneous Ricci solitons up to dimension 5, according to their presentation as homogeneous spaces. We obtain that they are all isometric to solvsolitons, and this in particular implies that the…

The nilpotent graph of a group $G$ is the simple and undirected graph whose vertices are the elements of $G$ and two distinct vertices are adjacent if they generate a nilpotent subgroup of $G$. Here we discuss some topological properties of…

Using a filtration on the Grothendieck ring of triangulated categories, we define the categorical dimension of a birational map between smooth projective varieties. We show that birational automorphisms of bounded categorical dimension form…

The (co)homological dimension of homomorphism $\phi:G\to H$ is the maximal number $k$ such that the induced homomorphism is nonzero for some $H$-module. The following theorems are proven: THEOREM 1. For every homomorphism $\phi:G\to H$ of a…

Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…

We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show…

Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal…

We prove that over any perfect field the plane Cremona group is generated by involutions.

We construct Cremona transformations of P^3 with bidegrees (d,e), where d<e^2+1, e< d^2+1 and d,e> 0.

It is shown that every separable abelian topological group is isomorphic with a topological subgroup of a monothetic group (that is, a topological group with a single topological generator). In particular, every separable metrizable abelian…

We give an explicit set of generators for various natural subgroups of the real Cremona group Bir_R(P^2). This completes and unifies former results by several authors.

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive…

We show that a hypersimple unidimensional theory that has a club of reducts, in the partial order of all countable reducts, that are coordinatized in finite rank, is supersimple.

It is proved that fundamental groups of boolean representable simplicial complexes are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension $\geq 2$. In the case of…

In this paper we give a characterization of the possible homology groups that can occur for compact simply connected cohomogeneity one manifolds in dimensions seven and lower.

We give a complete description of the distance relation on the graph of $4$-ary simplex codes of dimension $2$. This is a connected graph of diameter $3$. For every vertex we determine the sets of all vertices at distance $i\in\{1,2,3\}$…

We prove that the groups of orientation preserving quasiconformal or bilipschitz homeomorphisms of S^n are simple in dimensions 2 and higher.