On mod p Ap–spaces

Huang, Ruizhi; Wu, Jie

doi:10.2140/agt.2017.17.2125

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On mod $p$ $A_p$–spaces

Ruizhi Huang and Jie Wu

Algebraic & Geometric Topology 17 (2017) 2125–2144

DOI: 10.2140/agt.2017.17.2125

Abstract

We prove a necessary condition for the existence of an $A_{p}$ –structure on $mod p$ spaces, and also derive a simple proof for the finiteness of the number of $mod p$ $A_{p}$ –spaces of given rank. As a direct application, we compute a list of possible types of rank $3$ $mod p$ 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

Volume 17, issue 4 (2017)