i Register
In some senses, homotopy is marked as informal. Watch for register when choosing this word.
homotopy
/həˈmɑtəpi/
noun 5
Collocations
3ADJ.
so-called, so-called
HOMOTOPY + NOUN
algebra, exponent, formalisation
PREP.
in
Definitions
noun
1
A continuous deformation of one continuous function or map to another.
The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.
An integer M is called an exponent for the torsion of an abelian group G if M * (torsion of G) = 0. We say that M is a homotopy exponent for a space X if M is an exponent for πₖ (X) for all k.
2
The relationship between two continuous functions where homotopy from one to the other is evident.
3
Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).
4
A theory associating a system of groups with each topological space.
5
A system of groups associated with a topological space.
Thesaurus
Synonyms
Antonyms
Idioms & Phrases
Example Bank
301
The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.
Wiktionary02
An integer M is called an exponent for the torsion of an abelian group G if M * (torsion of G) = 0. We say that M is a homotopy exponent for a space X if M is an exponent for πₖ (X) for all k.
Wiktionary03
A graded Lie algebra arises from these maps via the Samelson product in homotopy, the so-called homotopy Lie algebra which is discussed below.
WiktionaryUsage Notes
Your note
not saved0 chars