2024-05-19   61813

Homotopy, Homotopy Groups, and Covering Spaces

Homotopy groups are examples of topological invariants: topologically equivalent spaces have the same homotopy groups. Roughly, the nth homotopy group of a topological space M expresses the inequivalent ways an n-sphere can be continuously mapped into M, regarding two such maps as equivalent if one can be continuously morphed into the other. The homotopy group with n=1 is called the fundamental group. This article introduces homotopy groups and the related concept of a covering space. A covering space E of M is like M but "unwrapped" so that E's fundamental group is only part of M's fundamental group.

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www.cphysics.org updated 2024-07-11