相关论文: The Henon Family: The Complex Horseshoe Locus and …
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
Zonotopes are a rich and fascinating family of polytopes, with connections to many areas of mathematics. In this article we provide a brief survey of classical and recent results related to lattice zonotopes. Our emphasis is on connections…
We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which the diffeomorphisms have arbitrarily large finite numbers of…
This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of…
We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain…
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the…
This thesis is split up into two parts: The first one concerns (pseudo)-holomorphic Hamiltonian systems, while the second part is about K\"ahler structures of complex coadjoint orbits. We begin the first part by investigating basic…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
We consider two well-known integrable systems on the plane using the concept of natural Poisson bivectors on Riemaninan manifolds. Geometric approach to construction of variables of separation and separated relations for the generalized…
A family of solutions of the Jacobi PDEs is investigated. This family is $n$-dimensional, of arbitrary nonlinearity and can be globally analyzed (thus improving the usual local scope of Darboux theorem). As an outcome of this analysis it is…
This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative…
In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson…
We characterize the (regular) holonomicity of Horn systems of differential equations under a hypothesis that captures the most widely studied classical hypergeometric systems.
This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of…
Families of smooth closed oriented 4-manifolds with a complex spin structure are studied by means of a family version of the Bauer--Furuta invariants in the context of parametrised stable homotopy theory, leading to a definition of…
We consider moduli spaces of plane quartics marked with various structures such as Cayley octads, Aronhold heptads, Steiner complexes and G\"opel subsets and determine their cohomology. This answers a series of questions of Jesse Wolfson.…
We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced…
The subject for investigation in this note is concerned with holomorphic Poisson structures on nilmanifolds with abelian complex structures. As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in…