Certain numbers on the groups of self-homotopy equivalences
DC Field | Value | Language |
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dc.contributor.author | Choi, Ho Won | - |
dc.contributor.author | Lee, Kee Young | - |
dc.date.accessioned | 2021-09-04T19:12:15Z | - |
dc.date.available | 2021-09-04T19:12:15Z | - |
dc.date.created | 2021-06-15 | - |
dc.date.issued | 2015-02-15 | - |
dc.identifier.issn | 0166-8641 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/94394 | - |
dc.description.abstract | For a connected based space X, let [X, X] be the set of all based homotopy classes of base point preserving self map of X and let 6(X) be the group of self-homotopy equivalences of X. We denote by A(#)(k) (X) the set of homotopy classes of self-maps of X that induce an automorphism of pi(i) (X) for i = 0,1, ..., k. That is, [f] is an element of A(#)(k) (X) if and only if pi(i)(f) : pi(i)(X) -> pi(i)(X) is an isomorphism for i = 0,1, ..., k. Then, E(X) subset of A(#)(k)(X) subset of [X, X] for a nonnegative integer k. Moreover, for a connected CW-complex X, we have E(X) = A(#)(X). In this paper, we study the properties of A(X) and discuss the conditions under which E(X) = A(#)(k) (X) and the minimum value of such k. Furthermore, we determine the value of k for various spaces, including spheres, products of spaces, and Moore spaces. (C) 2014 Elsevier B.V. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ELSEVIER SCIENCE BV | - |
dc.title | Certain numbers on the groups of self-homotopy equivalences | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Lee, Kee Young | - |
dc.identifier.doi | 10.1016/j.topol.2014.12.004 | - |
dc.identifier.scopusid | 2-s2.0-85027955066 | - |
dc.identifier.wosid | 000349811100005 | - |
dc.identifier.bibliographicCitation | TOPOLOGY AND ITS APPLICATIONS, v.181, pp.104 - 111 | - |
dc.relation.isPartOf | TOPOLOGY AND ITS APPLICATIONS | - |
dc.citation.title | TOPOLOGY AND ITS APPLICATIONS | - |
dc.citation.volume | 181 | - |
dc.citation.startPage | 104 | - |
dc.citation.endPage | 111 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordAuthor | Homotopy equivalence | - |
dc.subject.keywordAuthor | Self-closeness number | - |
dc.subject.keywordAuthor | k-Self equivalence | - |
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