Definition of "homotopy" [homotopy]

• A continuous deformation of one continuous function to another. (noun)
• A theory associating a system of groups to each topological space. (noun)
• A system of groups associated to a topological space. (noun)

Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License

• "Some details must be ironed out: for example, the investigation of loops which are very similar gives no insight into the structure of the space, so we work instead with sets of loops called homotopy classes One of the most useful tools in algebraic topology is the [[fundamental group]],"
• "(humorously) a dunce cap, its fundamental group is its set of path loops that has a useful characteristic known as "[[homotopy]]""
• "However, I find to stomach arguments that other completely useless things – like calculating the QCD beta function to n loops, or calculating the homotopy groups of spheres is somehow more worthy."