Related papers: Jonqui\`eres maps and $\mathrm{SL}(2;\mathbb{C})$-…

One introduces a class of projective parameterizations that resemble generalized de Jonqui\`eres maps. Any such parametrization defines a birational map $\mathfrak{F}$ of $\pp^n$ onto a hypersurface $V(F)\subset \pp^{n+1}$ with a strong…

Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, $x\to x+\omega~({\rm mod}~1)$, with rational rotation number $\omega$ are given. The consequences of the existence of such maps in families of maps is…

Let M be a smooth connected compact surface, P be either the real line R^1 or the circle S^1, and f:M-->P be a smooth mapping. In a previous series of papers for the case when f is a Morse map the author calculated the homotopy types of…

Let $f:(\mathbb{C}^n,0)\mapsto(\mathbb{C}^n,0)$ be a germ of an $n$-dimensional holomorphic map. Assume that the origin is an isolated fixed point of each iterate of $f$. Then $\{\mathcal{N}_q(f)\}_{q=1}^{\infty}$, the sequence of the…

We describe the cohomology ring $H^*(J_2;\mathbb{F}_3)$ both as subring of $H^*(3^{1+2}_+;\mathbb{F}_3)$ and with an abstract presentation. We also give its Poincar\'{e} series. We use as tool a spectral sequence for the strongly closed…

We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; these formulas involve a family of polynomials…

Finite tensor categories (FTCs) $\bf T$ are important generalizations of the categories of finite dimensional modules of finite dimensional Hopf algebras, which play a key role in many areas of mathematics and mathematical physics. There…

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when $G$ is a connected reductive complex algebraic group with simply-connected derived subgroup, two…

This is the second part of the article [math.KT/0408094]. In the first paper, we used the underlying coalgebra structure to develop a cyclic theory. In this paper we define a dual theory by using the algebra structure. We define a cyclic…

Explicit formulae are given for the saddle connection of an integrable family of standard maps studied by Y. Suris. When the map is perturbed this connection is destroyed, and we use a discrete version of Melnikov's method to give an…

We show that a circle and square of the same area in $\mathbb{R}^2$ are equidecomposable by translations using $\mathbf{\Delta}^0_2$ pieces. That is, pieces which are simultaneously $F_\sigma$ and $G_\delta$ sets. This improves a result of…

Let S be a compact connected oriented surface, whose boundary is connected or empty. A homology cylinder over the surface S is a cobordism between S and itself, homologically equivalent to the cylinder over S. The Y-filtration on the monoid…

Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…

Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $\eta\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated…

We generalize the notions of $\beta$- and $\lambda$-maps to general selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normality, extremal disconnectedness,…

In this paper we will study families of circle maps of the form $x\mapsto x+2\pi r + a f(x) \pmod{2\pi}$ and investigate how many periodic trajectories maps from this family can have for a "typical" function $f$ provided the parameter $a$…

This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

By a gradient-like flow on a closed orientable surface $M$, we mean a closed 1-form $\beta$ defined on $M$ punctured at a finite set of points (sources and sinks of $\beta$) such that there exists a Morse function $f$ on $M$, called an…

A main theme of the paper is a conjecture of Bloch-Kato on the image of $p$-adic regulator maps for a proper smooth variety $X$ over an algebraic number field $k$. The conjecture for a regulator map of particular degree and weight is…