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On spherical classes in the Z/2-homology of QS^n

Le : 28/10/2014 15h00
Par : Hadi ZARE (U. Tehran et IPM)
Lieu : I 001
Lien web :
Résumé : We consider the problem of determining spherical classes in H_*QS^n, especially in the case n=0. First, using stability arguments, we reprove (without using string operations) a result of Gérald Gaudens that almost any class which is the sum of decomposable classes in the stable homotopy ring maps trivially under the Hurewicz homomorphism h. For instance, this implies that the ideal generated by the homotopy groups of J maps trivially under h. Second, we determine the form of potential spherical classes, which in contrast to the first part, provides some opportunity to use string operations to eliminate classes. Third, we construct a "relation" from the set of spherical classes of length 2 to the set of maps detected by secondary operations. This is done using calculations by hand, and seems, somehow, to provide an inverse to the well-known Lannes-Zarati homomorphism. (All of this work is at the prime p=2).