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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On mod $p$ $A_p$–spaces

Ruizhi Huang and Jie Wu

Algebraic & Geometric Topology 17 (2017) 2125–2144
Abstract

We prove a necessary condition for the existence of an Ap–structure on modp spaces, and also derive a simple proof for the finiteness of the number of modp Ap–spaces of given rank. As a direct application, we compute a list of possible types of rank 3 modp homotopy associative H–spaces.

Keywords
$A_p$-space, $\psi$-operation, homotopy associative $H$-space, Steenrod powers, Adem relations
Mathematical Subject Classification 2010
Primary: 55P45, 55S25
Secondary: 55N15, 55P15, 55S05
References
Publication
Received: 11 February 2016
Revised: 9 December 2016
Accepted: 26 December 2016
Published: 3 August 2017
Authors
Ruizhi Huang
Department of Mathematics
National University of Singapore
10 Lower Kent Ridge Road
Singapore 119076
Singapore
Jie Wu
Department of Mathematics
National University of Singapore
10 Lower Kent Ridge Road
Singapore 119076
Singapore
http://www.math.nus.edu.sg/~matwujie