2018/09/19 by Grady, Daniel, Sati, Hisham · 1 citation
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.1809.07059
We provide several constructions in differential KO-theory. First, we construct a differential refinement of the A-genus and a pushforward leading to a Riemann-Roch theorem. We set up a differential refinement of the Atiyah-Hirzebruch spectral sequence (AHSS) for differential KO-theory and explicitly identify the differentials, including ones which mix geometric and topological data. We highlight the power of these explicit identifications by providing a characterization of forms in the image of the Pontrjagin character. Along the way, we fill gaps in the literature where K-theory is usually worked out leaving KO-theory essentially untouched. We also illustrate with examples and applications, including higher tangential structures, Adams operations, and a differential Wu formula.