The homotopy of L_2V(1) for the prime 3

Paul Goerss , Hans-Werner Henn (1) , Mark Mahowald

1 IRMA - Institut de Recherche Mathématique Avancée

Let V(1) be the Toda-Smith complex for the prime 3. We give a complete calculation of the homotopy groups of the L_2-localization of V(1) by making use of the higher real K-theory EO_2 of Hopkins and Miller and related homotopy fixed point spectra. In particular we resolve an ambiguity which was left in an earlier approach of Shimomura whose computation was almost complete but left an unspecified parameter still to be determined.

Mots clés: Stable homotopy theory

Domaines: Topologie algébrique [math.AT]

Paul Goerss, Hans-Werner Henn, Mark Mahowald. The homotopy of L_2V(1) for the prime 3. International Conference in Algebraic Topology, 2004, Isle of Skye, United Kingdom. ⟨hal-00129678⟩