{"oa_version":"Submitted Version","publisher":"Springer","abstract":[{"text":"Let X and Y be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group G. Assuming that Y is d-connected and dimX≤2d, for some d≥1, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps |X|→|Y|; the existence of such a map can be decided even for dimX≤2d+1. This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into Rn under the condition k≤23n−1. More generally, we present an algorithm that, given a lifting-extension problem satisfying an appropriate stability assumption, computes the set of all homotopy classes of solutions. This result is new even in the non-equivariant situation.","lang":"eng"}],"oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","volume":54,"date_updated":"2023-09-20T12:01:28Z","article_processing_charge":"No","scopus_import":"1","intvolume":"        54","department":[{"_id":"UlWa"}],"quality_controlled":"1","date_published":"2017-06-01T00:00:00Z","publication":"Discrete & Computational Geometry","month":"06","doi":"10.1007/s00454-016-9855-6","publication_identifier":{"issn":["01795376"]},"isi":1,"external_id":{"isi":["000400072700008"]},"year":"2017","title":"Algorithmic solvability of the lifting extension problem","page":"915 - 965","type":"journal_article","citation":{"chicago":"Čadek, Martin, Marek Krcál, and Lukáš Vokřínek. “Algorithmic Solvability of the Lifting Extension Problem.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00454-016-9855-6\">https://doi.org/10.1007/s00454-016-9855-6</a>.","ista":"Čadek M, Krcál M, Vokřínek L. 2017. Algorithmic solvability of the lifting extension problem. Discrete &#38; Computational Geometry. 54(4), 915–965.","mla":"Čadek, Martin, et al. “Algorithmic Solvability of the Lifting Extension Problem.” <i>Discrete &#38; Computational Geometry</i>, vol. 54, no. 4, Springer, 2017, pp. 915–65, doi:<a href=\"https://doi.org/10.1007/s00454-016-9855-6\">10.1007/s00454-016-9855-6</a>.","short":"M. Čadek, M. Krcál, L. Vokřínek, Discrete &#38; Computational Geometry 54 (2017) 915–965.","apa":"Čadek, M., Krcál, M., &#38; Vokřínek, L. (2017). Algorithmic solvability of the lifting extension problem. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-016-9855-6\">https://doi.org/10.1007/s00454-016-9855-6</a>","ama":"Čadek M, Krcál M, Vokřínek L. Algorithmic solvability of the lifting extension problem. <i>Discrete &#38; Computational Geometry</i>. 2017;54(4):915-965. doi:<a href=\"https://doi.org/10.1007/s00454-016-9855-6\">10.1007/s00454-016-9855-6</a>","ieee":"M. Čadek, M. Krcál, and L. Vokřínek, “Algorithmic solvability of the lifting extension problem,” <i>Discrete &#38; Computational Geometry</i>, vol. 54, no. 4. Springer, pp. 915–965, 2017."},"status":"public","_id":"1073","publist_id":"6309","date_created":"2018-12-11T11:50:00Z","language":[{"iso":"eng"}],"issue":"4","author":[{"full_name":"Čadek, Martin","first_name":"Martin","last_name":"Čadek"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek"},{"first_name":"Lukáš","last_name":"Vokřínek","full_name":"Vokřínek, Lukáš"}],"main_file_link":[{"url":"https://arxiv.org/abs/1307.6444","open_access":"1"}],"publication_status":"published"}