- homotopy theory
- мат.теория гомотопий
English-Russian scientific dictionary. 2008.
homotopy theory
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Rational homotopy theory — In mathematics, rational homotopy theory is the study of the rational homotopy type of a space, which means roughly that one ignores all torsion in the homotopy groups. It was started by Dennis Sullivan (1977) and Daniel Quillen (1969) … Wikipedia
A¹ homotopy theory — In algebraic geometry and algebraic topology, a branch of mathematics, A1 homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to… … Wikipedia
Stable homotopy theory — In mathematics, stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the… … Wikipedia
Spectrum (homotopy theory) — In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, all of which give the same homotopy category.Suppose we… … Wikipedia
Homotopy category — In mathematics, a homotopy category is a category whose objects are topological spaces and whose morphisms are homotopy classes of continuous functions. The homotopy category of all topological spaces is often denoted hTop or Toph.Homotopy… … Wikipedia
Homotopy group — In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The base point preserving maps from an n dimensional sphere (with base point) into a given space (with base point) are collected into equivalence… … Wikipedia
Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… … Wikipedia
Homotopy lifting property — In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a… … Wikipedia
Homotopy fiber — In mathematics, especially homotopy theory, the homotopy fiber is part of a construction of associating to an arbitrary continuous function of topological spaces f colon A o B a fibration.In particular, given such a map, define E f to be the set… … Wikipedia
Homotopy groups of spheres — In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure… … Wikipedia
Homotopy principle — In mathematics, the homotopy principle (or h principle) is a very general way to solve partial differential equations (PDEs), and more generally partial differential relations (PDRs). The h principle is good for underdetermined PDEs or PDRs, such … Wikipedia
