## Journal of the Mathematical Society of Japan

### Lifting to mod $2$ Moore spaces

#### Abstract

We try to investigate whether an element of order $2$ in homotopy groups of spheres has a lift to an element of homotopy groups of mod $2$ Moore spaces or not. A typical element of the affirmative property is Thomeier's element of $\pi_{8n+7}(S^{4n+3})$. And the Whitehead square $[l_{2n+1},l_{2n+1}]$ of the identity class $l_{2n+1}$ of $S^{2n+1}$ is a negative example except for $n=0,1$ and $3$.

#### Article information

Source
J. Math. Soc. Japan, Volume 52, Number 3 (2000), 515-533.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213107284

Digital Object Identifier
doi:10.2969/jmsj/05230515

Mathematical Reviews number (MathSciNet)
MR1760602

Zentralblatt MATH identifier
0960.55006

#### Citation

MORISUGI, Kaoru; MUKAI, Juno. Lifting to mod $2$ Moore spaces. J. Math. Soc. Japan 52 (2000), no. 3, 515--533. doi:10.2969/jmsj/05230515. https://projecteuclid.org/euclid.jmsj/1213107284