Constructing and calculating Adams operations on dualisable topological modular forms

Abstract: We construct Adams operations on the cohomology theory Tmf of topological modular forms; the first such stable operations on this cohomology theory. These Adams operations are then calculated on the Tmf-cohomology of spheres 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.