Constructing and calculating Adams operations on dualisable topological modular forms

We construct Adams operations \psi^{k} on the cohomology theory \mathrm{Tmf} of dualisable topological modular forms after inverting k ; the first such multiplicative stable operations on this cohomology theory. These Adams operations are then calculated on the homotopy groups of \mathrm{Tmf} using a combination of descent spectral sequences and Anderson duality. Applications of these operations are then given, including constructions of connective height 2 analogues of Adams summands and image-of- J spectra .