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Sep, 2019
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Homotopy Groups and Homotopy Sets

Homotopy groups are introduced by Hurewicz in 1935. Although the definition is fairly simple, it is very hard to determine homotopy groups in general.

Homotopy groups are algebraic invariants with emphasis on spheres and balls, and they are fundamental and important in the world of CW-complexes . For exotic spaces which do not have the homotopy type of CW-complexes, however, we need an alternative framework to work with. One of such examples is the Steenrod homotopy theory [ Mel ] .

Some people think that it is unnatural to restrict our attentions to continuous maps and study spaces of not-necessarily-continous maps .

References