On the structure of the RO(G)-graded homotopy of HM for cyclic p-groups

Sikora, Igor; Yan, Guoqi

doi:10.2140/agt.2025.25.2933

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

On the structure of the $RO(G)$-graded homotopy of $H\underline{M}$ for cyclic $p$-groups

Igor Sikora and Guoqi Yan

Algebraic & Geometric Topology 25 (2025) 2933–2980

DOI: 10.2140/agt.2025.25.2933

Abstract

We study the structure of the $R O (G)$ -graded homotopy Mackey functors of any Eilenberg–MacLane spectrum $H \underline{M}$ for $G$ a cyclic $p$ -group. When $\underline{R}$ is a Green functor, we define orientation classes $u_{V}$ for $H \underline{R}$ and deduce a generalized gold relation. We deduce the $a_{V}, u_{V}$ -isomorphism regions of the $R O (G)$ -graded homotopy Mackey functors and prove two induction theorems. As applications, we compute the positive cone of $H \underline{𝔸}$ , as well as the positive and negative cones of $H \underline{ℤ}$ . The latter two cones are essential to the slice spectral sequences of $M U^{((C_{2^{n}}))}$ and its variants.

Keywords

equivariant homotopy, $RO(G)$-graded homotopy groups, Eilenberg–MacLane spectra, cyclic $p$-groups

Mathematical Subject Classification

Primary: 55Q91

References

Publication

Received: 18 October 2023

Revised: 21 April 2024

Accepted: 17 June 2024

Published: 17 September 2025

Authors

Igor Sikora
Kraków University of Economics Krakow Poland

Guoqi Yan
Department of Mathematics University of Notre Dame Notre Dame, IN United States	Shanghai Center for Mathematical Sciences Fudan University Shanghai, China

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 5 (2025)