On the existence of the self map v_2^9 on the 
Smith-Toda complex V(1) at the prime 3

Mark Behrens
Department of Mathematics
University of Chicago
Chicago, IL 60637, U.S.A.
mbehrens@math.uchicago.edu

Satya Pemmaraju
Fixed Income Derivatives
UBS Warburg
Stamford, CT 06901, U.S.A.
Satya.Pemmaraju@ubsw.com

AMS Classification:  55Q51; 55Q45, 55T15

math.AT/0303223
submitted to proceedings of the Northwestern
University conference on algebraic topology, March 2002

Included EPS files:

assE2.eps
bss.eps
eo_2V1.eps
eo_2V1ASS.eps
extP.eps
splitting.eps

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Abstract 

Let V(1) be the Smith-Toda complex at the prime 3. We prove that there exists
a map v_2^9: \Sigma^{144}V(1) \to V(1) that is a K(2) equivalence. This map is
used to construct various v_2-periodic infinite families in the 3-primary
stable homotopy groups of spheres.