Topological complexity: Difference between revisions

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Line 13: 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 5.<ref>{{Cite ~~arXiv~~journal \|~~eprint~~arxiv = 1612.03133\|last1 = Cohen\|first1 = Daniel C.\|title = Topological ~~Complexity~~complexity of the Klein bottle\|last2 = Vandembroucq\|first2 = Lucile\|~~class~~ journal=Journal of Applied and Computational Topology ~~math.AT~~\|year = 2016\| volume=1 \| issue=2 \| pages=199–213 \| doi=10.1007/s41468-017-0002-0 }}</ref> ==References==