Homology, Homotopy and Applications

Torsion in finite $H$-spaces and the homotopy of the three-sphere

Piotr Beben and Stephen Theriault

Full-text: Open access

Abstract

Let $X$ be a 2-connected $p$-local finite $H$-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion i: $S^3 \underset {\longrightarrow}{i} X$ has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that $\pi_m(i )= 0$ for $m \geq 4$. Applications are made to Harper's rank 2 finite $H$-space and simple, simply-connected, compact Lie groups.

Article information

Source
Homology Homotopy Appl., Volume 12, Number 2 (2010), 25-37.

Dates
First available in Project Euclid: 28 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296223877

Mathematical Reviews number (MathSciNet)
MR2721030

Zentralblatt MATH identifier
1200.55013

Subjects
Primary: 55P45: $H$-spaces and duals 55Q52: Homotopy groups of special spaces

Keywords
H-space Harper’s space torsion Lie group three sphere

Citation

Beben, Piotr; Theriault, Stephen. Torsion in finite $H$-spaces and the homotopy of the three-sphere. Homology Homotopy Appl. 12 (2010), no. 2, 25--37. https://projecteuclid.org/euclid.hha/1296223877


Export citation