Time: 9h00, Wednesday, March 13, 2019
Location: Rom 612, Building A6, Institute of Mathematics
Abstract: The unstable Adams spectral sequence, allowing for passing from homological information to homotopical information, is one of the most powerful tool in Algebraic Topology. Therefore, the study of this particular spectral sequence is quite intensive. In this talk, we discuss about the unstable Adams spectral sequence for the stable special orthogonal group SO. The interesting fact is that, the homotopy groups of this space is well-known thanks to the Bott periodicity theorem. However, the homological information provided by the unstable Adams spectral sequence in this case is quite complicated and not yet understood. To study this phenomenon, Bousfield constructed a special spectral , in an algebraic way, that also converge to the homotopy groups of SO. Based on the construction of this spectral sequence, he conjectured that this spectral sequence coincides with the unstable Adams spectral sequence for SO. We will study the weaker conjecture on the comparision of only the input of these spectral sequences.