Translation for 'homotopy' from English to Russian

homotopy

гомотопия {ж}мат.

• The basic point is that sphere complements determine the homology, but not the homotopy type, in general.
• The stable homotopy category, or homotopy category of (CW) spectra is defined to be the category whose objects are spectra and whose morphisms are homotopy classes of maps between spectra.
• The higher homotopy groups of RP"n" are exactly the higher homotopy groups of "Sn", via the long exact sequence on homotopy associated to a fibration.
• Assembly maps exist for any homotopy invariant functor, by a simple homotopy-theoretical construction.
• A homotopy theory that studies simple-homotopy types is called simple homotopy theory.

• The homotopy groups are fundamental to homotopy theory, which in turn stimulated the development of model categories. It is possible to define abstract homotopy groups for simplicial sets.
• This is a homotopy invariant and it tells us which homotopy class the instanton belongs to.
• Both of these examples consist of reducing regular homotopy to homotopy; this has subsequently been substantially generalized in the homotopy principle (or "h"-principle) approach.
• Since the torus is an Eilenberg–MacLane space "K"("G", 1), its homotopy equivalences, up to homotopy, can be identified with automorphisms of the fundamental group); all homotopy equivalences of the torus can be realized by homeomorphisms – every homotopy equivalence is homotopic to a homeomorphism.
• Possible homotopy classes are controlled by the homotopy group [...].