Journal of the Mathematical Society of Japan

Self homotopy groups of Hopf spaces with at most three cells

Mamoru MIMURA and Hideaki ŌSHIMA

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Abstract

We prove that if X is aconnected H-space with at most three cells of positive dimension, then the self homotopy set of X becomes a group relative to the binary operation induced from any multiplication on X, and we determine it's group structure in some cases.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 71-92.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108352

Digital Object Identifier
doi:10.2969/jmsj/05110071

Mathematical Reviews number (MathSciNet)
MR1661032

Zentralblatt MATH identifier
0931.55005

Subjects
Primary: 55P45: $H$-spaces and duals
Secondary: 55Q05: Homotopy groups, general; sets of homotopy classes

Keywords
Hopf space self homotopy set

Citation

MIMURA, Mamoru; ŌSHIMA, Hideaki. Self homotopy groups of Hopf spaces with at most three cells. J. Math. Soc. Japan 51 (1999), no. 1, 71--92. doi:10.2969/jmsj/05110071. https://projecteuclid.org/euclid.jmsj/1213108352


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