The T-Algebra Spectral Sequence: Comparisons and Applications

Justin Noel
Thursday, July 25, 2013 - from 14:50 to 15:30
In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as $G$-spaces and $E_n$-ring spectra. In special cases, we will show that the Goerss-Hopkins spectral sequence and the $T$-algebra spectral sequence agree, although they differ in general. Under further hypotheses, we will show that these spectral sequences agree with the unstable Adams spectral sequence to obtain information about filtration and differentials. After reviewing immediate applications to unstable rational and $p$-adic homotopy theory we apply this spectral sequence to construct $E_\infty$ lifts of genera associated to cobordism theories.