Related papers: Topologies and structures of the Cremona groups

We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and $p$-Jordan property. In particular, we show that the Cremona group of rank $2$ over a field of…

We consider the topological complexity of subgroups of Artin's braid group consisting of braids whose associated permutations lie in some specified subgroup of the symmetric group. We give upper and lower bounds for the topological…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…

In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…

This short note deals with the conjugacy classes of monomial birational maps in the $n$-dimensional Cremona group, $n\geq 2$.

In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersection complex}, which is a quasi-isometry invariant. In this…

We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we…

Two divisors in $\P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. We produce infinitely many non equivalent divisorial embeddings of any variety of dimension at most 14. Then we study the…

We formulate a construction of type-I fracton models based on gauging planar subsystem symmetries of topologically ordered two dimensional layers that have been stacked in three ambient spatial dimensions. Via our construction, any defect…

We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$…

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space for n greater than 3. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and…

This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…

The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a non-commutative ring that is an analog of non-commutative field of two independent variables and prove that the Cremona group…

Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…

We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.

We show that every automorphism of the group $\mathcal{G}_n:= \textrm{Aut}(\mathbb{A}^n)$ of polynomial automorphisms of complex affine $n$-space $\mathbb{A}^n=\mathbb{C}^n$ is inner up to field automorphisms when restricted to the subgroup…

In this paper, we study the Grassmannian of n-dimensional subspaces of a 2n-dimensional vector space and its infinite-dimensional analogues. Such a Grassmannian can be endowed with two binary relations (adjacent and distant), with pencils…

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

In this article, we introduce the singular twin monoid and its corresponding group, constructed from both algebraic and topological perspectives. We then classify all complex homogeneous $2$-local representations of this constructed group.…