homotopy
/həˈmɑtəpi/
Word Rarity
Very rare
Frequency: Zipf frequency 2.18 in modern English
18
Scrabble Score
8
Letters
3
Syllables
6
Unique Chars
Meaning
noun
The relationship between two continuous functions where homotopy from one to the other is evident.
Uncountable
noun
Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).
Countable; Informal; Uncountable
Example Sentences
- "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."
- "A graded Lie algebra arises from these maps via the Samelson product in homotopy, the so-called homotopy Lie algebra which is discussed below."
- "2010, Vladimir G. Turaev, Homotopy Quantum Field Theory, European Mathematical Society, page xi, In this monograph we apply the idea of a TQFT to maps from manifolds to topological spaces. This leads us to a notion of a (d + 1)-dimensional homotopy quantum field theory (HQFT) which may be described as a TQFT for closed oriented d-dimensional manifolds and compact oriented (d + 1)-dimensional cobordisms endowed with maps to a given space X."
Etymology
From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs.
Origin
Word Breakdown
- Root: ὁμός
Regional Pronunciation
- American English: /həˈmɑtəpi/
Usage
Inflected Forms
Derived Forms
Phrases
homotopy category
homotopy class
homotopy equivalence
homotopy equivalent
homotopy fiber
homotopy fibre
homotopy group
homotopy invariant