Discussion of homotopy groups in computational topology:
Martin Čadek, Marek Krčál, Jiří Matoušek, Lukáš Vokřínek, Uli Wagner, Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension, SIAM J. Comput., 43(5), 1728–1780 (arXiv:1211.3093, doi:10.1137/120899029)
Martin Čadek, Marek Krčál, Jiří Matoušek, Lukáš Vokřínek, Uli Wagner, Extendability of continuous maps is undecidable, Discrete Comput Geom (2014) 51: 24 (arXiv:1302.2370, doi:10.1007/s00454-013-9551-8)
Marek Filakovsky, Peter Franek, Uli Wagner, Stephan Zhechev, Computing simplicial representatives of homotopy group elements, J Appl. and Comput. Topology (2018) 2: 177. (arXiv:1706.00380)
Discussion of Cohomotopy-sets in computational topology:
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