Topological complexity

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In mathematics, topological complexity of a topological space X (also denoted by TC(X)) is a topological invariant closely connected to the motion planning problem[ further explanation needed ], introduced by Michael Farber in 2003.

Contents

Definition

Let X be a topological space and be the space of all continuous paths in X. Define the projection by . The topological complexity is the minimal number k such that

Examples

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References

  1. Cohen, Daniel C.; Vandembroucq, Lucile (2016). "Topological Complexity of the Klein bottle". arXiv: 1612.03133 [math.AT].