Related papers: Functorial CW-approximation

We study topological aspects of the category of abstract Cuntz semigroups, termed Cu. We provide a suitable setting in which we are able to uniformly control how to approach an element of a Cu-semigroup by a rapidly increasing sequence.…

We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…

We construct a non-trivial homomorphism from the Guay's affine Yangian to the universal enveloping algebra of non-rectangular $W$-algebras of type $A$. In order to construct the homomorphism, we extend the Guay's affine Yangian and its…

Continuous Dynamic Time Warping (CDTW) measures the similarity of polygonal curves robustly to outliers and to sampling rates, but the design and analysis of CDTW algorithms face multiple challenges. We show that CDTW cannot be computed…

Let $w$ be an unbounded radial weight on the complex plane. We study the following approximation problem: find a proper holomorphic map $f: \mathbb{C}\to\mathbb{C}^n$ such that $|f|$ is equivalent to $w$. We give several characterizations…

The existing observational data on possible variations of fundamental physical constants (FPC) confirm more or less confidently only a variability of the fine structure constant $\alpha$ in space and time. A model construction method is…

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…

Consider the quasi-commutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of high-frequency…

Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as…

We investigate whether non-metrizable manifolds in various classes can be homotopy equivalent to a CW-complex (in short: heCWc), and in particular contractible. We show that a non-metrizable manifold cannot be heCWc if it has one of the…

We develop functoriality for Morse theory, namely, to a pair of Morse-Smale systems and a generic smooth map between the underlying manifolds we associate a chain map between the corresponding Morse complexes, which descends to the correct…

We extend the notion of amoeba to holomorphic almost periodic functions in tube domains. In this setting, the order of a function in a connected component of the complement to its amoeba is just the mean motion of this function. We also…

Let $G$ be a compact Lie group. (Compact) topological $G$-manifolds have the $G$-homotopy type of (finite-dimensional) countable $G$-CW complexes (2.5). This partly generalizes Elfving's theorem for locally linear $G$-manifolds [Elf96],…

The completion tower of a nonunital commutative ring is a classical construction in commutative algebra. In the setting of structured ring spectra as modeled by algebras over a spectral operad, the analogous construction is the homotopy…

In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we…

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to…

We prove that the native space of a Wu function is a dense subspace of a Sobolev space. An explicit characterization of the native spaces of Wu functions is given. Three definitions of Wu functions are introduced and proven to be…

The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…

For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This…