## Journal of the Mathematical Society of Japan

### Self homotopy groups of Hopf spaces with at most three cells

#### 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