In this note we establish the compatibility between the topological index in the differential K-theory of Freed-Lott and the analytic push-forward construction in the differential K-theory of Bunke-Schick by a direct computation.
"On the compatibility between the differential topological index and the analytic Bunke-Schick push-forward construction." Bull. Belg. Math. Soc. Simon Stevin 26 (2) 241 - 253, june 2019. https://doi.org/10.36045/bbms/1561687564