{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:50:47Z","timestamp":1740124247152,"version":"3.37.3"},"reference-count":3,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T00:00:00Z","timestamp":1585699200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T00:00:00Z","timestamp":1585699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100009934","name":"E\u00f6tv\u00f6s Lor\u00e1nd University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100009934","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We will present proofs for two conjectures stated in Rot (Homotopy classes of proper maps out of vector bundles, 2020. <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"http:\/\/arxiv.org\/abs\/1808.08073\">arXiv:1808.08073<\/jats:ext-link>). The first one is that for an arbitrary manifold <jats:italic>W<\/jats:italic>, the homotopy classes of proper maps <jats:inline-formula><jats:alternatives><jats:tex-math>$$W\\times \\mathbb {R}^n\\rightarrow \\mathbb {R}^{k+n}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>W<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:msup><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mi>n<\/mml:mi><\/mml:msup><mml:mo>\u2192<\/mml:mo><mml:msup><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> stabilise as <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\rightarrow \\infty $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and the second one is that in a stable range there is a Pontryagin\u2013Thom type bijection for proper maps <jats:inline-formula><jats:alternatives><jats:tex-math>$$W\\times \\mathbb {R}^n\\rightarrow \\mathbb {R}^{k+n}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>W<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:msup><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mi>n<\/mml:mi><\/mml:msup><mml:mo>\u2192<\/mml:mo><mml:msup><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The second one actually implies the first one and we shall prove the second one by giving an explicit construction.\n<\/jats:p>","DOI":"10.1007\/s10998-020-00327-0","type":"journal-article","created":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T11:02:43Z","timestamp":1585738963000},"page":"259-268","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stable Pontryagin\u2013Thom construction for proper maps"],"prefix":"10.1007","volume":"80","author":[{"given":"Andr\u00e1s","family":"Cs\u00e9pai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,4,1]]},"reference":[{"key":"327_CR1","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1090\/S0002-9939-1961-0133785-8","volume":"12","author":"K Nomizu","year":"1961","unstructured":"K. Nomizu, H. Ozeki, The existence of complete Riemannian metrics. Proc. Am. Math. Soc. 12, 889\u2013891 (1961)","journal-title":"Proc. Am. Math. Soc."},{"key":"327_CR2","unstructured":"T.O. Rot, Homotopy Classes of Proper Maps Out of Vector Bundles (2019), preprint arXiv:1808.08073"},{"key":"327_CR3","doi-asserted-by":"publisher","first-page":"399","DOI":"10.2140\/gt.2001.5.399","volume":"5","author":"C Rourke","year":"2001","unstructured":"C. Rourke, B. Sanderson, The compression theorem I. Geom. Topol. 5, 399\u2013429 (2001)","journal-title":"Geom. Topol."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-020-00327-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-020-00327-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-020-00327-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T23:42:34Z","timestamp":1617234154000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-020-00327-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,1]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["327"],"URL":"https:\/\/doi.org\/10.1007\/s10998-020-00327-0","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2020,4,1]]},"assertion":[{"value":"1 April 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}