Embeddability of simplicial complexes is undecidable
M. Filakovský, U. Wagner, S.Y. Zhechev, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 767–785.

Algorithmic aspects of homotopy theory and embeddability
S.Y. Zhechev, Algorithmic Aspects of Homotopy Theory and Embeddability, Institute of Science and Technology Austria, 2019.

Computing simplicial representatives of homotopy group elements
M. Filakovský, P. Franek, U. Wagner, S.Y. Zhechev, Journal of Applied and Computational Topology 2 (2018) 177–231.