Related papers: A note on weak conjugacy for homeomorphisms of sur…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
The holomorphy conjecture states roughly that Igusa's zeta function associated to a hypersurface and a character is holomorphic on $\mathbb{C}$ whenever the order of the character does not divide the order of any eigenvalue of the local…
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 use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…
We introduce a crossed module of piecewise linear surfaces and study the signature homomorphism, defined as the surface holonomy of a universal translation invariant $2$-connection. This provides a transform whereby surfaces are represented…
We describe structural properties of strongly connected finite directed graphs, that are invariants of the topological conjugacy of their Markov-Dyck shifts. For strongly connected finite directed graphs with these properties topological…
In this paper, we prove that two normal complex surface germs that are inner bilipschitz--but not necessarily orientation-preserving--homeomorphic, have in fact the same oriented topological type and the same minimal plumbing graph. Along…
In this review we present some recent extensions of the method of the weakly conjugate operator. We illustrate these developments through examples of operators on graphs and groups.
We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface $S$ of genus at least $2$. In particular, we prove they are exactly the automorphisms of a graph of essential quasicircles…
We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its…
We discuss the isomorphism problem for ergodic actions of locally compact groups. In particular we show that the conjugacy relation is not Borel for ergodic measure preserving actions of indicable groups.
We demonstrate that the proper homotopy equivalence relation for locally finite graphs is Borel complete. Furthermore, among the infinite graphs, there is a comeager equivalence class. As corollaries, we obtain the analogous results for the…
The Epstein-Baer theory of curve isotopies is basic to the remarkable theorem that homotopic homeomorphisms of surfaces are isotopic. The groundbreaking work of R. Baer was carried out on closed, orientable surfaces and extended by D. B. A.…
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of…
Given a dimension function $\omega$, we define a notion of an $\omega$-vector weighted digraph and an $\omega$-equivalence between them. Then we establish a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes…
We investigate the mapping class group of an orientable $\omega$-bounded surface. Such a surface splits, by Nyikos's Bagpipe Theorem, into a union of a bag (a compact surface with boundary) and finitely many long pipes. The subgroup…
We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces $(\Sigma,g_1)$ and $(\Sigma,g_2)$ when the cone angles of $g_1$ and $g_2$ are different and smaller than $\pi$. When the cone…
We define character varieties with non-connected structure groups of finitely presented discrete groups and study some basic aspects, such as generic conjugacy classes and relation with fixed points in character varieties with connected…
We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.
We show that, for a closed non-orientable surface $F$, an automorphism of $H_1(F,\Z)$ is induced by a homeomorphism of $F$ if and only if it preserves the (mod 2) intersection pairing. We shall also prove the corresponding result for…