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Gustavo Granja - On self maps of HPn

GUSTAVO GRANJA, Department of Mathematics, MIT, Cambridge, Massachusetts  02139, USA
On self maps of HPn

In 1975, Feder and Gitler computed the action of the Adams operations on the K-theory of HPn and used this to get restrictions on the possible degrees of self maps. They conjectured that all the integers satisfying these restrictions are degrees of actual self maps. The conjecture is known to be true for n=2,3 and $\infty$. We show that it also holds for n=4,5 by using computations by Curtis and Mahowald of the unstable Adams spectral sequence for S3 and explain why this gives qualitatively stronger evidence for the conjecture.


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