Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

A universal property for $Sp(2)$ at the prime $3$

Pages: 1 – 15

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n1.a1


Jelena Grbić (School of Mathematics, University of Manchester, United Kingdom)

Stephen Theriault (Department of Mathematical Sciences, University of Aberdeen, Scotland, United Kingdom)


We study a universal property of $Sp(2)$ in the category of $3$-local homotopy associative, homotopy commutative $H$-spaces. We show that while $Sp(2)$ fails to be universal in the full category, there is a subcategory in which it is universal for its $7$-skeleton.


$H$-space, $H$-map, Whitehead product

2010 Mathematics Subject Classification

Primary 55P45. Secondary 55Q15.

Published 1 January 2009