EVENT DETAILS AND ABSTRACT

Title: Maps of homotopy T-algebras
Speaker: Justin Noel
Speaker Info: MPI Bonn
Brief Description:
Special Note:
Abstract:

If T is a (nice) monad acting on a (very nice) model category C we obtain a (nice) model category of T-algebras in C. Moreover, the monad T descends in this situation to a monad T^\prime in the homotopy category of C and we have a forgetful functor from the derived category of T-algebras to T^\prime-algebras in hoC. In the case that C is spectra and T-algebras in C are E_\infty ring spectra, this forgetful functor lands in H_\infty ring spectra. To analyze this functor Niles Johnson and I constructed a spectral sequence which computes the homotopy of the space of T-algebra maps and whose edge homomorphism is this forgetful functor. Naturally occurring examples show that this functor is in general, neither full nor faithful. We also provide some examples when this map is an isomorphism.