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.
(uncountable) The relationship between two continuous functions where homotopy from one to the other is evident.
(informal) Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes).
(topology) A theory associating a system of groups with each topological space.
(topology) A system of groups associated with a topological space.
Source: en.wiktionary.orgAn equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence : if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it. Source: Internet
An introductory exercise is to classify the uppercase letters of the English alphabet according to homeomorphism and homotopy equivalence. Source: Internet
A quasigroup homotopy from Q to P is a triple (α, β, γ) of maps from Q to P such that : for all x, y in Q. A quasigroup homomorphism is just a homotopy for which the three maps are equal. Source: Internet
A stronger assumption is necessary; in dimensions four and higher there are simply-connected, closed manifolds which are not homotopy equivalent to an n-sphere. Source: Internet
Chow, Mallet-Paret, and Yorke gave a conceptually similar path-following version of the homotopy proof which extends to a wide variety of related problems. Source: Internet
For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere? Source: Internet