SELF-HOMOTOPY EQUIVALENCES RELATED TO COHOMOTOPY GROUPS
- Authors
- Choi, Ho Won; Lee, Kee Young; Oh, Hyung Seok
- Issue Date
- 3월-2017
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- self-homotopy equivalence; cohomotopy group; Moore space; co-Moore space
- Citation
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.54, no.2, pp.399 - 415
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 54
- Number
- 2
- Start Page
- 399
- End Page
- 415
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/84340
- DOI
- 10.4134/JKMS.j150765
- ISSN
- 0304-9914
- Abstract
- Given a topological space X and a non -negative integer k, we study the self-homotopy equivalences of X that do not change maps from X to n -sphere S-n homotopically by the composition for all n >= k. We denote by epsilon(K)(X) the set of all homotopy classes of such self-homotopy equivalences. This set is a dual concept of epsilon(k) (X), which has been studied by several authors. We prove that if X is a finite CW complex, there are at most a finite number of distinguishing homotopy classes epsilon(k) (X), whereas epsilon(k) (X) may not be finite. Moreover, we obtain concrete computations of epsilon(k) (X) to show that the cardinal of epsilon(k)(X) is finite when X is either a Moore space or co-Moore space by using the self -closeness numbers.
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Collections - College of Science and Technology > Data Computational Sciences in Division of Applied Mathematical Sciences > 1. Journal Articles
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