Related papers: Parametrised topological complexity of group epimo…
In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…
In comparison to graphs, combinatorial methods for the isomorphism problem of finite groups are less developed than algebraic ones. To be able to investigate the descriptive complexity of finite groups and the group isomorphism problem, we…
We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…
We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (Conner-Herfort-Pavesic:…
We study free topological groups defined over uniform spaces in some subclasses of the class NA of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free…
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We study certain topological problems that are inspired by applications to autonomous robot manipulation. Consider a continuous map $f\colon X\to Y$, where $f$ can be a kinematic map from the configuration space $X$ to the working space $Y$…
One generally expects that the techniques of arboreal singularities and gluing of local differential graded categories will result in a useful global invariant for all Weinstein manifolds. In this paper we construct explicit models for the…
We employ Massey products to find sharper lower bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces $X$ for which the topological complexity $\TC(X)$ (defined to be…
Using the ordered analogue of Farley-Sabalka's discrete gradient field on the configuration space of a graph, we unravel a levelwise behavior of the generators of the pure braid group on a tree. This allows us to generalize Farber's…
For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…
Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly…
Contact manifolds are odd-dimensional smooth manifolds endowed with a maximally non-integrable field of hyperplanes. They are intimately related to symplectic manifolds, i.e. even-dimensional smooth manifolds endowed with a closed…
We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…
Stefan M$\ddot{\mathrm{u}}$ller posed the problem "Do Hofer's metrics on the group of Hamiltonian diffeomorphism and the one of Hamiltonian homeomorphisms (Hameomorphisms) correspond?". Let $(M,\omega)$ be a compact exact symplectic…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…
In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…
We study the monodromy diffeomorphism of Milnor fibrations of isolated complex surface singularities, by computing the family Seiberg--Witten invariant of Seifert-fibered Dehn twists using recent advances in monopole Floer homology. More…