Topology and its Applications最新文献

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Cohomology rings of oriented Grassmann manifolds G˜2t,4

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-03-04 DOI: 10.1016/j.topol.2025.109318

Uroš A. Colović, Milica Jovanović , Branislav I. Prvulović

We give a description of the mod 2 cohomology algebra of the oriented Grassmann manifold

{\tilde{G}}_{2^{t}, 4}

as the quotient of a polynomial algebra by a certain ideal. In the process we find a Gröbner basis for that ideal, which we then use to exhibit an additive basis for

H^{⁎} ({\tilde{G}}_{2^{t}, 4}; Z_{2})

引用次数: 0

Properties of equi-Baire 1 and equi-Lebesgue families of functions

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-03-03 DOI: 10.1016/j.topol.2025.109317

Marek Balcerzak , Ľubica Holá , Dušan Holý

We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behavior of equi-Baire 1 and equi-Lebesgue families with respect to pointwise and uniform convergence. In particular, we obtain a criterion for a choice of a uniformly convergent subsequence from a sequence of functions that form an equi-Baire 1 family, which solves a problem posed in [3]. Finally, we discuss the notion of equi-cliquishness and relations between equi-Baire 1 families and sets of equi-continuity points.

引用次数: 0

Handle numbers of guts of sutured manifolds and nearly fibered knots

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-28 DOI: 10.1016/j.topol.2025.109316

Kenneth L. Baker , Fabiola Manjarrez-Gutiérrez

Extending Haken's Theorem to product annuli and disks for Heegaard splittings of sutured manifolds, we show that the handle number of an irreducible sutured manifold equals the handle number of its guts. We further show that reduced sutured manifolds with torus boundary contained in

S^{3}

fall in to three types that generalize the three models of guts of knots that are nearly fibered in the instanton or Heegaard Floer sense. In conjunction with these results and another concerning uniqueness of incompressible Seifert surfaces, we show that while many nearly fibered knots have handle number 2 and a unique incompressible Seifert surface, some have handle number 4 and others have extra incompressible Seifert surfaces. Examples of nearly fibered knots with non-isotopic incompressible Seifert surfaces are exhibited.

引用次数: 0

Infinite families of standard Cappell-Shaneson homotopy 4-spheres

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-25 DOI: 10.1016/j.topol.2025.109293

Kazunori Iwaki

Cappell-Shaneson homotopy 4-spheres (CS spheres) are potential counterexamples of the smooth 4-dimensional Poincaré conjecture. The simplest CS spheres was proven to be diffeomorphic to the standard 4-sphere in 2010. Another family of CS spheres was proven to be diffeomorphic to the standard 4-sphere in 2023. In this paper, we prove more CS spheres are standard. We give 145 new infinite families of CS spheres which are diffeomorphic to the standard 4-sphere.

引用次数: 0

Function spaces of Lawson-compact algebraic domains

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-25 DOI: 10.1016/j.topol.2025.109295

Wei Luan , Qingguo Li

In this paper, we investigate function spaces of Lawson-compact algebraic domains. It is proved that a dcpo is a Lawson-compact algebraic domain iff there is an approximate identity consisting of Scott-continuous kernel operators whose images are prefinite algebraic domains. Using this fact, we obtain the following results:

(1)
The function space from a bifinite domain to a Lawson-compact algebraic domain is a Lawson-compact algebraic domain.
(2)
An algebraic domain X is bifinite iff $[X \to L]$ is a domain for each domain L.
(3)
The function space from a Lawson-compact algebraic domain to a bifinite domain (not necessarily pointed) is a bifinite domain.

引用次数: 0

Linear and smooth oriented equivalence of orthogonal representations of finite groups 有限群正交表示的线性和光滑定向等价性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-24 DOI: 10.1016/j.topol.2025.109292

Luis Eduardo García-Hernández , Ben Williams

Let Γ be a finite group. We prove that if

ρ, ρ^{'} : Γ \to O (4)

are two representations that are conjugate by an orientation-preserving diffeomorphism of

S^{3}

, then they are conjugate by an element of

SO (4)

. In the process, we prove that if

G \subset O (4)

is a finite group, then exactly one of the following is true: the elements of G have a common invariant 1-dimensional subspace in

R^{4}

; some element of G has no invariant 1-dimensional subspace; or G is conjugate to a specific group

K \subset O (4)

of order 16.

引用次数: 0

Topological and dimensional properties of univoque bases in double-base expansions

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-24 DOI: 10.1016/j.topol.2025.109294

Yuecai Hu , Rafael Alcaraz Barrera , Yuru Zou

Given two real numbers

q_{0}, q_{1}

with

q_{0}, q_{1} > 1

satisfying

q_{0} + q_{1} \geq q_{0} q_{1}

, we call a sequence

(d_{i})

with

d_{i} \in {0, 1}

(q_{0}, q_{1})

-expansion or a double-base expansion of a real number x if

x = \sum_{i = 1}^{\infty} \frac{d_{i}}{q_{d_{1}} q_{d_{2}} \dots q_{d_{i}}} .

When

q_{0} = q_{1} = q

, the set of univoque bases is given by the set of q's such that

x = 1

has exactly one

(q, q)

-expansion. The topological, dimensional and symbolic properties of such sets and their corresponding sequences have been intensively investigated. In our research, we study the topological and dimensional properties of the set of univoque bases for double-base expansions. This problem is more complicated, requiring new research strategies. Several new properties are uncovered. In particular, we show that the set of univoque bases in the double base setting is a meagre set with full Hausdorff dimension.

引用次数: 0

Singular homology of roots of unity

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-21 DOI: 10.1016/j.topol.2025.109291

Nikola Milićević

We extend some basic results from the singular homology theory of topological spaces to the setting of Čech's closure spaces. We prove analogues of the excision and Mayer-Vietoris theorems and the Hurewicz theorem in dimension one. We use these results to calculate examples of singular homology groups of spaces that are not topological but are often encountered in applied topology, such as simple undirected graphs. We focus on the singular homology of roots of unity with closure structures arising from considering nearest neighbors. These examples can then serve as building blocks along with our Mayer-Vietoris and excision theorems for computing the singular homology of more complex closure spaces.

引用次数: 0

Many subalgebras of P(ω)/fin

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-19 DOI: 10.1016/j.topol.2025.109280

Klaas Pieter Hart

In answer to a question on Mathoverflow we show that the Boolean algebra

P (ω) / fin

contains a family

{B_{X} : X \subseteq c}

of subalgebras with the property that

X \subseteq Y

implies

B_{Y}

is a subalgebra of

B_{X}

and if

X ⊈ Y

then

B_{Y}

is not embeddable into

B_{X}

. The proof proceeds by Stone duality and the construction of a suitable family of separable zero-dimensional compact spaces.

引用次数: 0

Completely Scott closed set and its applications

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications

Pub Date : 2025-02-19 DOI: 10.1016/j.topol.2025.109283

Licong Sun, Bin Pang

In this paper, we propose a concept of completely Scott closed sets and use it to study links between convex spaces and continuous lattices. Firstly, we take three equivalent approaches to construct a convex space from a continuous lattice. Secondly, we construct an adjunction between the category of convex spaces and the opposite category of continuous lattices via completely Scott closed sets. This adjunction exactly induces the concept of sober convex spaces which gives rise to a categorical duality between them and algebraic lattices. Finally, we prove that completely Scott closed sets form a monad over the category of convex spaces and obtain an isomorphism between the category of sober convex spaces and the Eilenberg–Moore category of this monad.

引用次数: 0

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