Related papers: Lattice structure on bounded homomorphisms between…
In this work we study the topology of holomorphic rank two bundles over complex surfaces. We consider bundles that are constructed by glueing and show that under certain conditions the topology of the bundle does not depend on the glueing.…
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
We classify surjective lattice homomorphisms $W\to W'$ between the weak orders on finite Coxeter groups. Equivalently, we classify lattice congruences $\Theta$ on $W$ such that the quotient $W/\Theta$ is isomorphic to $W'$. Surprisingly,…
Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…
We construct a ring homomorphism comparing the tautological ring, fixing a point, of a closed smooth manifold with that of its stabilisation by $S^{2a} \times S^{2b}$.
We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…
Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from potentially singular complex algebraic surfaces and complex curves inside them. We prove that knot lattice…
Johnson and Livingston have characterized peripheral structures in homomorphs of knot groups. We extend their approach to the case of links. The main result is an algebraic characterization of all possible peripheral structures in certain…
Let X, Y, and Z be topological modules over a topological ring R. In this paper, we introduce three different classes of bounded bigroup homomorphisms from X \times Y into Z with respect to the three different uniform convergence…
If $L$ is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex $\Delta(L)$ (definition recalled). Lattice-theoretically, the resulting object is a subdirect…
On objects of a triangulated category with a stability condition, we construct a topology.
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new one. We also propose several conjectures about its…
We introduce the concept of a topological J-group and determine for many important examples of topological groups if they are topological J-groups or not. Besides other results, we show that the underlying topological space of a pathwise…
We study locally conformal symplectic (LCS) structures of the second kind on a Lie algebra. We show a method to build new examples of Lie algebras admitting LCS structures of the second kind starting with a lower dimensional Lie algebra…
We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. This feature offers…
In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact…