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http://dx.doi.org/10.4134/JKMS.j160434

FACTORIZATION OF CERTAIN SELF-MAPS OF PRODUCT SPACES  

Jun, Sangwoo (Department of Mathematics Korea University)
Lee, Kee Young (Department of Mathematics Korea University)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1231-1242 More about this Journal
Abstract
In this paper, we show that, under some conditions, self-maps of product spaces can be represented by the composition of two specific self-maps if their induced homomorphism on the i-th homotopy group is an automorphism for all i in some section of positive integers. As an application, we obtain closeness numbers of several product spaces.
Keywords
reducible; k-reducible; self-homotopy equivalence; self-closeness number;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 M. Arkowitz, The group of self-homotopy equivalences - a survey, Lecture Notes in Math. Vol. 1425, 170-203, Springer, New York, 1990.
2 M. Arkowitz, Introduction to Homotopy Theory, Springer, New York Dordrecht Heidelberg London, 2010.
3 P. I. Booth and P. R. Heath, On the groups ${\varepsilon}(X{\times}Y)$ and ${\varepsilon}_B^B(X{\times}_BY)$, In Group of Self-Equivalences and Related Topics, ed. R. A. Piccinini, 17-31, Springer LNM 1425, 1990.
4 H. Choi and K. Lee, Certain self homotopy equivalences on wedge product on Moore spaces, Pacific J. Math. 272 (2014), no. 1, 35-57.   DOI
5 P. Pavesic, Self-homotopy equivalences of product spaces, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), no. 1, 181-197.   DOI
6 H. Choi and K. Lee, Certain numbers on the groups of self-homotopy equivalences, Topology Appl. 181 (2015), 104-111.   DOI
7 P. R. Heath, On the group ${\varepsilon}(X{\times}Y)$ of self homotopy equivalences of a product, Quaestiones Math. 19 (1996), no. 3-4, 433-451.   DOI
8 K. Lee, The groups of self pair homotopy equivalences, J. Korea Math. Soc. 43 (2006), no. 3, 491-506.   DOI
9 P. Pavesic, Self fibre homotopy equivalences of fibred products, Topology Appl. 102 (2000), no. 2, 169-180.   DOI
10 P. Pavesic, Reducibility of self-homotopy equivalences, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 2, 389-413.   DOI
11 A. J. Sieradski, Twisted self-homotopy equivalences, Pacific J. Math. 34 (1970), 789-802.