相关论文: Obstructions for automorphic quasiregular maps and…

We prove that the recently shown cohomological obstruction for quasiregular ellipticity has a generalization in the theory of quasiregular values. More specifically, if $M$ is a closed, connected, and oriented Riemannian $n$-manifold, and…

Let $f\colon M \to M$ be a uniformly quasiregular self-mapping of a compact, connected, and oriented Riemannian $n$-manifold $M$ without boundary, $n\ge 2$. We show that, for $k \in \{0,\ldots, n\}$, the induced homomorphism $f^* \colon…

$\Gamma$-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting $\Gamma$-structures are free over odd degree generators. We prove that this…

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\Gamma <G$ and $\Lambda < G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $\Gamma$ into…

An automorphism of a graph is called quasi-semiregular if it fixes a unique vertex of the graph and its remaining cycles have the same length. This kind of symmetry of graphs was first investigated by Kutnar, Malni\v{c}, Mart\'{i}nez and…

A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. In this paper, applying Tutte's algebraic representation of map, new ideas for enumerating non-equivalent orientable or non-orientable maps of graph are…

Let $f: S^2 \to S^2$ be an expanding branched covering map of the sphere to itself with finite postcritical set $P_f$. Associated to $f$ is a canonical quasisymmetry class $\GGG(f)$ of Ahlfors regular metrics on the sphere in which the…

We prove that, if $\Gamma$ is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of $\Gamma$ of order at least $6$, or the number of vertices of $\Gamma$ is bounded above by an absolute…

Let $M$ be a closed, oriented, and connected Riemannian $n$-manifold, for $n\ge 2$, which is not a rational homology sphere. We show that, for a non-constant and non-injective uniformly quasiregular self-map $f\colon M\to M$, the…

In a previous paper, we proved that a quasi-isometric map $f:X\longrightarrow Y$ between two pinched Hadamard manifolds $X$ and $Y$ is within bounded distance from a unique harmonic map. We extend this result to maps $f:\Gamma\backslash…

In this expository paper we discuss several properties on closed aspherical parabolic ${\sfG}$-manifolds $X/\Gamma$. These are manifolds $X/\Gamma$, where $X$ is a smooth contractible manifold with a parabolic ${\sfG}$-structure for which…

We provide the existence, for every complex rational smooth affine curve $\Gamma$, of a linear action of $\mathrm{Aut}(\Gamma)$ on the affine 3-dimensional space $\mathbb{A}^3$, together with a $\mathrm{Aut}(\Gamma)$-equivariant closed…

Let $f\colon M\to N$ be a proper map between two aspherical compact orientable 3-manifolds with empty or toroidal boundary. We assume that $N$ is not a closed graph-manifold. Suppose that $f$ induces an epimorphism on fundamental groups. We…

We give a proof, based on thermodynamic formalism, of a theorem in bounded cohomology extending a foundational result of Burger and Monod: if $\Gamma$ is an irreducible uniform lattice in a non-compact connected semisimple Lie group of real…

Let $X$ be an algebraic surface with $\mathcal{L}$ an ample line bundle on $X$. Let $\Gamma(X, \mathcal{L})$ be the \emph{geometric monodromy} group associated to family of nonsingular curves in $X$ that are zero loci of sections of…

For a locally finite, connected graph $\Gamma$, let $\operatorname{Map}(\Gamma)$ denote the group of proper homotopy equivalences of $\Gamma$ up to proper homotopy. Excluding sporadic cases, we show $\operatorname{Aut}(S(M_\Gamma)) \cong…

Let $M$ be a closed, oriented, smooth $4-$manifold with intersection form $\Gamma$, $A(\Gamma)$ the automorphism group of $\Gamma$ and $D(M)$ the subgroup induced by orientation-preserving diffeomorphisms of $M$. In this note we study the…

A nonpolycyclic nilpotent-by-cyclic group Gamma can be expressed as the HNN extension of a finitely-generated nilpotent group N. The first main result is that quasi-isometric nilpotent-by-cyclic groups are HNN extensions of quasi-isometric…

Let $\Gamma$ be a finitely generated group of matrices over $\mathbb{C}$. We construct an isometric action of $\Gamma$ on a complete CAT(0) space $X$ such that the restriction of this action to any subgroup of $\Gamma$ containing no…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…