#### Volume 17, issue 2 (2017)

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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 $Y:={M}_{2}\left(1\right)\wedge C\eta$ admits eight ${v}_{1}$-self-maps of periodicity $1$. These eight self-maps admit four different cofibers, which we denote by ${A}_{1}\left[ij\right]$ for $i,j\in \left\{0,1\right\}$. We show that each of these four spectra admits a ${v}_{2}$-self-map of periodicity $32$.

 This paper is dedicated to the memory of Mark Mahowald \textup(1931–2013)
##### Keywords
stable homotopy, $v_2$-periodicity
Primary: 55Q51
##### Supplementary material

Additional tables and input files for Bruner's Ext program

##### 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