Topological complexity: Difference between revisions

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*If <math>F(\R^m,n)</math> is the [[Configuration space (mathematics)|configuration space]] of ''n'' distinct points in the Euclidean ''m''-space, then

::<math>TC(F(\R^m,n))=\begin{cases} 2n-1 & \mathrm{for\,\, {\it m}\,\, odd} \\ 2n-2 & \mathrm{for\,\, {\it m}\,\, even.} \end{cases}</math>

*The topological complexity of the [[Klein bottle]] is 54.<ref>{{Cite arXiv |eprint = 1612.03133|last1 = Cohen|first1 = Daniel C.|title = Topological Complexity of the Klein bottle|last2 = Vandembroucq|first2 = Lucile|class = math.AT|year = 2016}}</ref>

==References==