相关论文: On Generalization of Homotopy of Words and Its App…
A general equivariant shape theory for arbitrary $G$-spaces in the case of a compact group $G$ is constructed by using the method of pseudometrics suggested by Yu. M. Smirnov as early as in 1985 at the fifth Tiraspol symposium on general…
We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer…
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
We investigate cobordisms of free knots. Free knots and links are also called homotopy classes of Gauss words and phrases. We define a new strong invariant of free knots which allows to detect free knots not cobordant to the trivial one.
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
The correspondence between definable connected groupoids in a theory $T$ and internal generalised imaginary sorts of $T$, established by Hrushovski in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics, 2012], is…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
In this paper we develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the…
We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona…
The paper is the survey of the modern results and applications of the theory of homotopes. The notion of a well-tempered element in an associative algebra is introduced and it is proven that the category of representations of the homotope…
We propose in this paper a method for measuring the similarity between ontological concepts and terms. Our metric can take into account not only the common words of two strings to compare but also other features such as the position of the…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
An injective word over a finite alphabet $V$ is a sequence $w=v_1v_2\cdots v_t$ of distinct elements of $V$. The set $\mathrm{inj}(V)$ of injective words on $V$ is partially ordered by inclusion. A complex of injective words is the order…
The intended model of the homotopy type theories used in Univalent Foundations is the infinity-category of homotopy types, also known as infinity-groupoids. The problem of higher structures is that of constructing the homotopy types needed…
This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…
The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical…
We present an Eilenberg-Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…