Related papers: Parametrised topological complexity of group epimo…
We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…
In this paper, we obtain an upper bound on the higher topological complexity of the total spaces of fibrations. As an application, we improve the usual dimensional upper bound on higher topological complexity of total spaces of some sphere…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These theorems characterize ultragraphs for which the topological full group of an associated groupoid is an isomorphism invariant. These results extend…
In this article, we study the complexity of weighted team definability for logics with team semantics. This problem is a natural analogue of one of the most studied problems in parameterized complexity, the notion of weighted…
In this article, we investigate the cobordism maps on periodic Floer homology (PFH). In the first part of the paper, we define the cobordism maps on PFH via Seiberg Witten theory as well as the isomorphism between PFH and Seiberg Witten…
We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work \cite{CHKR} that such mappings allow for cavitations and fractures singularities but fulfill a suitable…
We extend the adiabatic limit formula for eta-invariants by Bismut-Cheeger and Dai to Seifert fibrations. Our formula contains a new contribution from the singular fibres that takes the form of a generalised Dedekind sum. As an application,…
We prove a number of results concerning monomorphisms, epimorphisms, dominions and codominions in categories of coalgebras. Examples include: (a) representation-theoretic characterizations of monomorphisms in all of these categories that…
In a previous article, we introduced notions of finiteness obstruction, Euler characteristic, and L^2-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homotopy colimits of…
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…
The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the…
Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal…
We introduce a new quasi-isometry invariant for finitely generated groups and show that every group with this property admits a subshift which is effectively closed by patterns and that cannot be realized as the topological factor of any…
We obtain many results and solve some problems about feebly compact paratopological groups. We obtain necessary and sufficient conditions for such a group to be topological. One of them is the quasiregularity. We prove that each…
We prove that a topological group is isomorphic to the real line if and only if it is a one-parameteric, metrizable, and not monothetic. This result is used in the authors' other paper to prove that one-parametric groups in strictly convex…
The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…
We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.
We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of hyperbolic group on a…