Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

Self-maps of spaces in fibrations

Pages: 289 – 313

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a15

Authors

Nobuyuki Oda (Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka, Japan)

Toshihiro Yamaguchi (Faculty of Education, Kochi University, Kochi, Japan)

Abstract

Self-maps of spaces in fibrations which appear in Postnikov systems are studied. The results are applied to obtain relations among self-homotopy equivalences of spaces in those fibrations to prove inequalities among self-closeness numbers of those spaces. Making use of the models of Sullivan, self-closeness numbers of rational spaces are also examined and some examples of rational spaces are studied precisely.

Keywords

self-homotopy equivalence, fibration, self-closeness number, Sullivan model

2010 Mathematics Subject Classification

55P10, 55P62, 55Q05, 55R05

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The first author was partly supported by JSPS KAKENHI Grant Number JP15K04884.

Received 6 February 2018

Received revised 5 April 2018

Published 27 June 2018