{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T06:49:13Z","timestamp":1765608553344},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,2,13]],"date-time":"2017-02-13T00:00:00Z","timestamp":1486944000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s00454-016-9855-6","type":"journal-article","created":{"date-parts":[[2017,2,13]],"date-time":"2017-02-13T13:49:10Z","timestamp":1486993750000},"page":"915-965","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Algorithmic Solvability of the Lifting-Extension Problem"],"prefix":"10.1007","volume":"57","author":[{"given":"Martin","family":"\u010cadek","sequence":"first","affiliation":[]},{"given":"Marek","family":"Kr\u010d\u00e1l","sequence":"additional","affiliation":[]},{"given":"Luk\u00e1\u0161","family":"Vok\u0159\u00ednek","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,2,13]]},"reference":[{"key":"9855_CR1","doi-asserted-by":"publisher","unstructured":"Bredon, G.E.: Equivariant Cohomology Theories. Lecture Notes in Mathematics, vol. 34. Springer, Berlin (1967)","DOI":"10.1007\/BFb0082690"},{"key":"9855_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/1969664","volume":"65","author":"EH Brown","year":"1957","unstructured":"Brown, E.H.: Finite computability of Postnikov complexes. Ann. Math. 65, 1\u201320 (1957)","journal-title":"Ann. Math."},{"key":"9855_CR3","unstructured":"\u010cadek, M.,\u00a0Kr\u010d\u00e1l, M., Vok\u0159\u00ednek, L.:\u00a0 Algorithmic solvability of the lifting-extension problem (extended version). http:\/\/arxiv.org\/abs\/1307.6444 (2013)"},{"issue":"17","key":"9855_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2597629","volume":"61","author":"M \u010cadek","year":"2014","unstructured":"\u010cadek, M., Kr\u010d\u00e1l, M., Matou\u0161ek, J., Sergeraert, F., Vok\u0159\u00ednek, L., Wagner, U.: Computing all maps into a sphere. J. ACM 61(17), 1\u201344 (2014)","journal-title":"J. ACM"},{"key":"9855_CR5","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1137\/120899029","volume":"43","author":"M \u010cadek","year":"2014","unstructured":"\u010cadek, M., Kr\u010d\u00e1l, M., Matou\u0161ek, J., Vok\u0159\u00ednek, L., Wagner, U.: Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension. SIAM J. Comput. 43, 1728\u20131780 (2014)","journal-title":"SIAM J. Comput."},{"key":"9855_CR6","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/s00454-013-9551-8","volume":"51","author":"M \u010cadek","year":"2014","unstructured":"\u010cadek, M., Kr\u010d\u00e1l, M., Matou\u0161ek, J., Vok\u0159\u00ednek, L., Wagner, U.: Extendability of continuous maps is undecidable. Discrete Comput. Geom. 51, 24\u201366 (2014)","journal-title":"Discrete Comput. Geom."},{"key":"9855_CR7","doi-asserted-by":"publisher","unstructured":"Crabb, M.,\u00a0James, I.: Fibrewise Homotopy Theory. Springer Monographs in Mathematics. Springer, London (1998)","DOI":"10.1007\/978-1-4471-1265-5"},{"key":"9855_CR8","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/B978-044481779-2\/50003-1","volume-title":"Handbook of Algebraic Topology","author":"WG Dwyer","year":"1995","unstructured":"Dwyer, W.G., Spalinski, J.: Homotopy theories and model categories. In: James, I.M. (ed.) Handbook of Algebraic Topology, pp. 73\u2013126. Elsevier, Amsterdam (1995)"},{"key":"9855_CR9","doi-asserted-by":"publisher","first-page":"49","DOI":"10.2307\/1969702","volume":"60","author":"S Eilenberg","year":"1954","unstructured":"Eilenberg, S., MacLane, S.: On the groups $$H(\\Pi,n)$$ H ( \u03a0 , n ) , II. Methods of computation. Ann. Math. 60, 49\u2013139 (1954)","journal-title":"Ann. Math."},{"key":"9855_CR10","doi-asserted-by":"publisher","first-page":"313","DOI":"10.5817\/AM2012-5-313","volume":"48","author":"M Filakovsk\u00fd","year":"2012","unstructured":"Filakovsk\u00fd, M.: Effective chain complexes for twisted products. Arch. Math. (Brno) 48, 313\u2013322 (2012)","journal-title":"Arch. Math. (Brno)"},{"key":"9855_CR11","unstructured":"Filakovsk\u00fd, M.: Algorithmic construction of the Postnikov tower for diagrams of simplicial sets. Thesis. https:\/\/is.muni.cz\/th\/211334\/prif_d\/THESIS_Marek_Filakovsky.pdf"},{"key":"9855_CR12","unstructured":"Filakovsk\u00fd, M.,\u00a0Vok\u0159\u00ednek, L.: Are two given maps homotopic? An algorithmic viewpoint. http:\/\/arxiv.org\/abs\/1312.2337 (2013)"},{"key":"9855_CR13","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1216\/RMJ-2012-42-2-353","volume":"42","author":"G Friedman","year":"2012","unstructured":"Friedman, G.: An elementary illustrated introduction to simplicial sets. Rocky Mt. J. Math. 42, 353\u2013423 (2012)","journal-title":"Rocky Mt. J. Math."},{"key":"9855_CR14","unstructured":"Hirschhorn, P.S.: Model Categories and Their Localizations. Mathematical Surveys and Monographs, vol. 99. American Mathematical Society, Providence, RI (2003)"},{"key":"9855_CR15","volume-title":"Using the Borsuk\u2013Ulam Theorem","author":"J Matou\u0161ek","year":"2003","unstructured":"Matou\u0161ek, J.: Using the Borsuk\u2013Ulam Theorem. Springer, Berlin (2003)"},{"key":"9855_CR16","doi-asserted-by":"publisher","first-page":"259","DOI":"10.4171\/JEMS\/252","volume":"13","author":"J Matou\u0161ek","year":"2011","unstructured":"Matou\u0161ek, J., Tancer, M., Wagner, U.: Hardness of embedding simplicial complexes in $${\\mathbb{R}}^{d}$$ R d . J. Eur. Math. Soc. 13, 259\u2013295 (2011)","journal-title":"J. Eur. Math. Soc."},{"key":"9855_CR17","unstructured":"May, J.P.: Simplicial Objects in Algebraic Topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago (1992)"},{"key":"9855_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01109713","volume":"120","author":"JF McClendon","year":"1971","unstructured":"McClendon, J.F.: Obstruction theory in fiber spaces. Math. Z. 120, 1\u201317 (1971)","journal-title":"Math. Z."},{"key":"9855_CR19","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1215\/ijm\/1256052280","volume":"16","author":"CA Robinson","year":"1972","unstructured":"Robinson, C.A.: Moore-Postnikov systems for non-simple fibrations. Ill. J. Math. 16, 234\u2013242 (1972)","journal-title":"Ill. J. Math."},{"key":"9855_CR20","unstructured":"Rubio, J.,\u00a0Sergeraert, F.: Constructive homological algebra and applications. http:\/\/arxiv.org\/abs\/1208.3816 (2012) (Written in 2006 for a MAP Summer School at the University of Genova)"},{"key":"9855_CR21","first-page":"93","volume":"13","author":"W Shih","year":"1962","unstructured":"Shih, W.: Homologie des espaces fibres. Publ. Math. l\u2019IH\u00c9S 13, 93\u2013176 (1962)","journal-title":"Publ. Math. l\u2019IH\u00c9S"},{"key":"9855_CR22","doi-asserted-by":"publisher","unstructured":"Stasheff, J.: $$H$$ H -Spaces From a Homotopy Point of View. Lecture Notes in Mathematics, vol. 161. Springer, Berlin (1970)","DOI":"10.1007\/BFb0065896"},{"key":"9855_CR23","doi-asserted-by":"publisher","first-page":"359","DOI":"10.5817\/AM2013-5-359","volume":"49","author":"L Vok\u0159\u00ednek","year":"2013","unstructured":"Vok\u0159\u00ednek, L.: Computing the abelian heap of unpointed stable homotopy classes of maps. Arch. Math. (Brno) 49, 359\u2013368 (2013)","journal-title":"Arch. Math. (Brno)"},{"key":"9855_CR24","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1090\/conm\/617\/12311","volume":"617","author":"L Vok\u0159\u00ednek","year":"2014","unstructured":"Vok\u0159\u00ednek, L.: Constructing homotopy equivalences of chain complexes of free $${\\mathbb{Z}}G$$ Z G -modules. Contemp. Math. 617, 279\u2013296 (2014)","journal-title":"Contemp. Math."},{"key":"9855_CR25","doi-asserted-by":"publisher","first-page":"323","DOI":"10.5817\/AM2014-5-323","volume":"50","author":"L Vok\u0159\u00ednek","year":"2014","unstructured":"Vok\u0159\u00ednek, L.: Heaps and unpointed stable homotopy theory. Arch. Math. (Brno) 50, 323\u2013332 (2014)","journal-title":"Arch. Math. (Brno)"},{"issue":"1","key":"9855_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00454-016-9835-x","volume":"57","author":"L Vok\u0159\u00ednek","year":"2017","unstructured":"Vok\u0159\u00ednek, L.: Decidability of the extension problem for maps into odd-dimensional spheres. Discrete Comput. Geom. 57(1), 1\u201311 (2017)","journal-title":"Discrete Comput. Geom."},{"key":"9855_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02564408","volume":"42","author":"C Weber","year":"1967","unstructured":"Weber, C.: Plongements de polyedres dans le domaine metastable. Comment. Math. Helv. 42, 1\u201327 (1967)","journal-title":"Comment. Math. Helv."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-016-9855-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-016-9855-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-016-9855-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T16:20:15Z","timestamp":1568823615000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-016-9855-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,13]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["9855"],"URL":"https:\/\/doi.org\/10.1007\/s00454-016-9855-6","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,13]]}}}