Related papers: Deformations with fibre constancy
In this paper the new model of plastic deformation is constructed. For classification of plastic statuses the theory of knot is used.
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string…
Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case…
We use a knot invariant, namely the Tristram--Levine signature to study deformations of singular points of plane curves. We find a bound on the sum of M numbers over all singularities of a generic fiber in terms of the M number of the…
We study one parameter deformations of a pair consisting of an analytic singular space $X_0$ and a function $f_0$ on it, in case this defines an isolated singularity. We prove, under general conditions, a bouquet decomposition of the Milnor…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…
In this article we investigate rigidity properties of integrable area-preserving twist maps of the cylinder. More specifically, we prove that if a deformation of the standard integrable map preserves rotational invariant circles (i.e.,…
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of…
This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed…
The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often,…
In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions…
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
We describe explicitly the possible degenerations of a class of double Kodaira fibrations in the moduli space of stable surfaces. Using deformation theory we also show that under some assumptions we get a connected component of the moduli…
We show that complex symplectic structures need not be preserved under small deformations, and we find sufficient conditions for this to happen. We study various cohomologies of compact complex symplectic manifolds, obtaining some…