We give a shorter proof of Lemma 1.9 from Goodwillie, Calculus III, which is the key step in proving that the construction P_nF gives an n-excisive functor.
We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the building complex associated to level 3 structures at the prime 2. Finally, we note the existence of a number of connective models of the spectrum TMF(Gamma_0(3)).
Explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum are given, without detailed proofs.
