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/həˈmɑtəpi/ · noun
(topology) 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.
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.
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.
Use homotopy when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Homotopy means (topology) A continuous deformation of one continuous function or map to another..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.
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