Related papers: Isometric Embeddings in Bounded Cohomology

We study general properties of holomorphic isometric embeddings of complex unit balls $\mathbb B^n$ into bounded symmetric domains of rank $\ge 2$. In the first part, we study holomorphic isometries from $(\mathbb B^n,kg_{\mathbb B^n})$ to…

The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the…

We give a general criterion for the (bounded) simplicity of the automorphism groups of certain countable structures and apply it to show that the isometry group of the Urysohn space modulo the normal subgroup of bounded isometries is a…

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

We study the regularity of the isometric embedding X: (B(O,r),g) -> (R3, gcan) of a 2-ball with nonnegatively curved C4 metric into R3. Under the assumption that X can be expressed in the graph form, we show X is C2,1 near P, which is…

We investigate the relationship between finite groups and incidence geometries through their automorphism structures. Building upon classical results on the realizability of groups as automorphism groups of graphs, we develop a general…

We prove that the continuous cohomology of $\text{Isom}^+(\mathbb{H}^n)$ can be measurably realized on the boundary of hyperbolic space. This implies in particular that for $\text{Isom}^+(\mathbb{H}^n)$ the comparison map from continuous…

The fine curve graph was introduced to study homeomorphism group of surfaces. In this paper we study the topology of the Gromov boundary of this graph for closed surfaces with higher genus. We first prove a bounded geodesic image theorem…

We describe a construction for embeddings of complete graphs where the dual has a cutvertex and the genus is close to the minimum genus of the primal graph. When the number of vertices is congruent to 5 modulo 12, we further guarantee that…

We show that for singular hypersurfaces, a version of their genus-zero Gromov-Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups, a construction which is more amenable to computation and easier…

Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichm\"uller space, right-angled Artin groups, and many other cubical groups. Given such a space $\mathcal X$, we build…

We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological…

In this paper, we generalize the embedded homology groups of hypergraphs initially given in [S. Bressan, J. Li, S. Ren, and J. Wu, The embedded homology of hypergraphs and applications, Asian J. Math. 23(3)(2019) 479-500] and study the…

In this paper, we introduce geometric technique of working with skew-framed manifolds. It allows us to study stable homotopy groups of some Thom spaces by geometric means. We schematically describe how our results (which are also of…

In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…

We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of…

We introduce a graded homology theory for graded \'etale groupoids. For $\mathbb Z$-graded groupoids, we establish an exact sequence relating the graded zeroth-homology to non-graded one. Specialising to the arbitrary graph groupoids, we…

For two bounded domains in the complex plane whose semigroups of analytic endomorphisms are isomorphic, Eremenko proved in 1993 that the isomorphism is given as a conjugation by a conformal or anticonformal map. In the present paper we…

The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…

We prove an extension to the simplicial Nerve Lemma which establishes isomorphism of persistent homology groups, in the case where the covering spaces are filtered. While persistent homology is now widely used in topological data analysis,…