A condensed proof of the differential Grothendieck-Riemann-Roch theorem
  We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is well defined and a condensed proof of the R/Z Grothendieck-Riemann-Roch theorem. 
Man-Ho Ho
math.DG math.KT