Related papers: Geometric equivalence among smooth map germs

In this paper, we study formal mappings between smooth generic submanifolds in multidimensional complex space and establish results on finite determination, convergence and local biholomorphic and algebraic equivalence. Our finite…

The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for…

This thesis introduces the notion of "relative gerbes" for smooth maps of manifolds, and discusses their differential geometry. The equivalence classes of relative gerbes are classified by the relative integral cohomology in degree three.…

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…

In this paper we introduce a homotopy theoretic technique for proving that the $K$-theoretic assembly map is an equivalence. It is an extension of the methods used to prove split injectivity of the assembly and applies to any geometrically…

Let(X,d) be a metric space that has a directed graph G such that the sets V(G) and E(G) are respectively vertices and edges corresponding to X. We obtain sufficient conditions for the existence of an G-approximate best proximity pair of the…

Given a graph $\Gamma$, one may conside the set $X$ of its vertices as a metric space by assuming that all edges have length one. We consider two versions of homology theory of $\Gamma$ and their $K$-theory counterparts -- the $K$-theory of…

Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar…

In this paper we consider germs of smooth Levi flat hypersurfaces, under the following notion of local equivalence: S_1 ~ S_2 if their one-sided neighborhoods admit a biholomorphism smooth up to the boundary. We introduce a simple invariant…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a…

We extend several techniques and theorems from geometric group theory so that they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). A second way that we generalize earlier results is by eliminating freeness…

Let $M$ be a smooth surface in $\mathbb R^3$ (or a complex surface in $\mathbb C^3$) and $k\geq 2$ be an integer. At any point on $M$ and for any plane in $\mathbb R^3$, we construct a holomorphic map-germ $(\mathbb C^2,0)\to(\mathbb…

Given a measurable space (X, M) there is a (Galois) connection between sub-sigma-algebras of M and equivalence relations on X. On the other hand equivalence relations on X are closely related to congruences on stochastic relations. In…

We define the category of $G_2$-structures over a Riemannian 7-manifold $M$ and present an isomorphism between this category and a full subcategory of the category of octonion algebras over the ring of smooth real-valued functions…

Using only basic topological properties of real algebraic sets and regular morphisms we show that any injective regular self-mapping of a real algebraic set is surjective. Then we show that injective morphisms between germs of real…

It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…

This is a survey of recent works on the germ-equivalence problem of minimal rational curves on uniruled projective manifolds. Our main interest is when the associated varieties of minimal rational tangents form an isotrivial family of…

For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.