Related papers: Fibers of monotone maps of finite distortion

We study composed map germs with respect to their local fibrations. Under most general conditions, inspired by the tameness condition that was introduced recently, we prove the existence of singular tube fibrations, and we determine the…

Let $f$ be a polynomial map from $\mathbb R^m$ to $\mathbb R^n$ with $m>n>0$ and $t_0$ be a regular value of $f$. For a small open ball $D_{t_0}$ centered at $t_0$, we show that the map $f:f^{-1}(D_{t_0})\to D_{t_0}$ is a Serre fibration if…

This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…

For mappings of finite distortion actively investigated last 15--20 years, problems of a so-called lower order are discussed. It is proved that, mappings with finite length distortion $f:D\rightarrow {\Bbb R}^n,$ $n\ge 2,$ which have…

For warped products with harmonic curvature, nonconstant warping functions $\phi$, and compact two-dimensional bases $(M,h)$, we establish a dichotomy: either the Gaussian curvature $K$ of the metric $g=\phi^{-2}h$ is constant and negative,…

In this paper, we prove that in the system of bending flows on the moduli space of polygons with fixed side lengths introduced by Kapovich and Millson, the singular fibers are isotropic homogeneous submanifolds. The proof covers the case…

Around 1960, R. Palais and J. Cerf proved a fundamental result relating spaces of diffeomorphisms and imbeddings of manifolds: If V is a submanifold of M, then the map from Diff(M) to Imb(V,M) that takes f to its restriction to V is locally…

We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal…

Milnor's fibration theorem and its generalizations play a central role in the study of singularities of complex and real analytic maps. In the complex analytic case, the Milnor fibration on the sphere is always given by the normalized map…

The Hopf index, a topological invariant that quantifies the linking of preimage fibers, is fundamental to the structure and stability of hopfions. In this work, we propose a new mathematical framework for modeling hopfions with high Hopf…

The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to Manifold Approximate Fibration. We define obstructions in algebraic K-theory.…

We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to prove a uniformization result for compact metric surfaces by…

We show that a sufficient condition for the weak limit of a sequence of $W^1_q$-homeomorphisms with finite distortion to be almost everywhere injective for $q \geq n-1$, can be stated by means of composition operators. Applying this result,…

This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the…

We study the boundary $L_t$ of the Milnor fiber for the reduced holomorphic germs $f:(\Bbb C^3,0) \rightarrow (\Bbb C,0)$ having a non-isolated singularity at $0$. We prove that $L_t$ is a graph manifold by using a new technique of…

Topological structure of minimal sets is studied for a dynamical system $(E,F)$ given by a fibre-preserving, in general non-invertible, continuous selfmap $F$ of a graph bundle $E$. These systems include, as a very particular case,…

Let $X$ be a regular curve and let $f: X\to X$ be a monotone map. In this paper, nonwandering set of $f$ and the structure of special $\alpha$-limit sets for $f$ are investigated. We show that AP$(f)= \textrm{R}(f) =\Omega(f)$, where…

We obtain constraints on the topology of families of smooth $4$-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation…

It is well known that two-dimensional mappings preserving a rational elliptic fibration, like the Quispel-Roberts-Thompson mappings, can be deautonomized to discrete Painlev\'e equations. However, the dependence of this procedure on the…

We introduce a new model for elliptic fibrations endowed with a Mordell-Weil group of rank one. We call it a Q$_7(\mathscr{L},\mathscr{S})$ model. It naturally generalizes several previous models of elliptic fibrations popular in the…