Related papers: Birational maps preserving the contact structure o…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

We show the existence of polynomial maps which have a regular bifurcation value, while over a neighbourhood of this value the fibres are connected and diffeomorphic.

In this note we observe, answering a question of Eliashberg and Thurston, that all contact structures on a closed oriented 3-manifold are $C^\infty$-deformations of foliations.

In this note we present two equivalent definitions for the genus of a birational map X --> Y between smooth complex projective 3-folds. The first one is the definition introduced in 1973 by M. A. Frumkin, the second one was recently…

We study the groups of biholomorphic and bimeromorphic automorphisms of conic bundles over certain compact complex manifolds of algebraic dimension zero.

We obtain all coset $n$-valued topological groups on $S^3$ and $\mathbb{R}P^3$, arising from compact Lie groups Sp(1) and SO(3) and there finite groups of automorphisms.

We study z-automorphisms of the polynomial algebra K[x,y,z] and the free associative algebra K<x,y,z> over a field K, i.e., automorphisms which fix the variable z. We survey some recent results on such automorphisms and on the corresponding…

Let $\mathsf P$ be an operad acted upon by a group $G$, and let $\mathsf Q=\mathsf P\rtimes G$ be the corresponding framed operad. We relate the homotopy automorphism groups of $\mathsf P$ and $\mathsf Q$. We apply the result to compute the…

We identify the algebra of regular functions on the space of quartic polynomials in three complex variables invariant under SL(3,C) with an algebra of meromorphic automorphic forms on the complex 6-ball. We also discuss the underlying…

Let $\mathcal{E}(X)$ be the group of homotopy classes of self homotopy equivalences for a connected CW complex $X$. We observe two classes of maps $\mathcal{E}$-maps and co-$\mathcal{E}$-maps. They are defined as the maps $X\to Y$ that…

In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…

We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method…

The present article investigates Sp(3) structures on 14-dimensional Riemannian manifolds, a continuation of the recent study of manifolds modeled on rank two symmetric spaces (here: SU(6)/Sp(3)). We derive topological criteria for the…

We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the (usual) motivic invariants vanish for birational…

Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…

A combinatorial Morse structure encodes a mapping class for a surface with boundary, and the data may be efficiently represented via a Morse diagram. This diagram determines an open book decomposition of a 3-manifold, and hence, a contact…

In this paper we classify all potentially G-birationally rigid del Pezzo threefolds of degree 4 and their automorphism groups and prove the G-birational rigidity of one of them

We survey some recent results on biconservative surfaces in $3$-dimensional space forms $N^3(c)$ with a special emphasis on the $c=0$ and $c=1$ cases. We study the local and global properties of such surfaces, from extrinsic and intrinsic…

We determine the symmetries and reversing symmetries within G, the group of real planar polynomial automorphisms, of area-preserving nonlinear polynomial maps L in generalised standard form, L: x'=x+p(y), y'=y+q(x'), where p and q are…