On the periodic v2–self-map of A1

Bhattacharya, Prasit; Egger, Philip; Mahowald, Mark

doi:10.2140/agt.2017.17.657

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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

DOI: 10.2140/agt.2017.17.657

Abstract

The spectrum $Y : = M_{2} (1) \land C η$ admits eight $v_{1}$ -self-maps of periodicity $1$ . These eight self-maps admit four different cofibers, which we denote by $A_{1} [i j]$ for $i, j \in {0, 1}$ . 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

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

Volume 17, issue 2 (2017)