Related papers: Manifold structures in regular irreducible algebra…

In this paper we extend the classical theory of combinatorial manifolds to the non-homogeneous setting. NH-manifolds are polyhedra which are locally like Euclidean spaces of varying dimensions. We show that many of the properties of…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…

We develop a unified representation theory for the categories of finite subsets and relation-preserving maps of highly homogeneous relational structures classified by Cameron. For any commutative coefficient ring $k$, we extend the…

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring,…

We study monoids generated by various combinations of idempotents and one- or two-sided units of an infinite partial Brauer monoid. This yields a total of eight such monoids, each with a natural characterisation in terms of relationships…

In this paper the concept of local embeddability into finite structures (being LEF) for the class of semigroups is expanded with investigations of non-LEF structures, a closely related generalising property of local wrapping of finite…

The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real…

We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix…

Let phi: P^1 --> P^1 be a rational map defined over a field K. We construct the moduli space M_d(N) parameterizing conjugacy classes of degree-d maps with a point of formal period N and present an algebraic proof that M_2(N) is…

We consider closed manifolds that possess a so called rank one ray structure. That is a (flat) affine structure such that the linear part is given by the products of a diagonal transformation and a commuting rotation. We show that closed…

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…

We establish the equivalence between the family of closed uniformly regular Riemannian manifolds and the class of complete manifolds with bounded geometry.

A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly independent. In this paper, we give some lower bounds of the dimension of the ambient Euclidean space for complex…

This paper shows that the Grassmann Manifolds $G_{\bf F}(n,N)$ can all be imbedded in an Euclidean space $M_{\bf F}(N)$ naturally and the imbedding can be realized by the eigenfunctions of Laplacian $\triangle$ on $G_{\bf F}(n,N)$. They are…

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space $\mathscr F_q(r, d)$ of singular foliations of codimension $q$ and degree $d$ on the complex…

Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if…

Let $R$ be a finite commutative ring with unity $1_R$ and $k \in R$. Properties of one-sided $k$-orthogonal $n \times n$ matrices over $R$ are presented. When $k$ is idempotent, these matrices form a semigroup structure. Consequently new…

We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…

This paper is devoted to a systematic study of the geometry of nondegenerate $\bbR^n$-actions on $n$-manifolds. The motivations for this study come from both dynamics, where these actions form a special class of integrable dynamical systems…