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On the periodic $v_2$–self-map of $A_1$

Prasit Bhattacharya, Philip Egger and Mark Mahowald

Algebraic & Geometric Topology 17 (2017) 657–692
Abstract

The spectrum Y := M2(1) Cη admits eight v1-self-maps of periodicity 1. These eight self-maps admit four different cofibers, which we denote by A1[ij] for i,j {0,1}. We show that each of these four spectra admits a v2-self-map of periodicity 32.

This paper is dedicated to the memory of Mark Mahowald \textup(1931–2013)

Keywords
stable homotopy, $v_2$-periodicity
Mathematical Subject Classification 2010
Primary: 55Q51
Supplementary material

Additional tables and input files for Bruner's Ext program

References
Publication
Received: 21 January 2015
Revised: 28 June 2016
Accepted: 8 August 2016
Published: 14 March 2017
Authors
Prasit Bhattacharya
Department of Mathematics
University of Notre Dame
106 Hayes-Healy Hall
Notre Dame, IN 46556
United States
Philip Egger
Department of Mathematics
Pennsylvania State University
235 McAllister
University Park, PA 16802
United States
Mark Mahowald
Department of Mathematics
Northwestern University
Evanston, IL 60208
United States