The differential analytic index in Simons-Sullivan differential K-theory

TL;DR

This paper introduces the Simons-Sullivan differential analytic index by translating the Freed-Lott index through explicit isomorphisms and proves a differential Grothendieck-Riemann-Roch theorem within this framework.

Contribution

It defines a new differential analytic index in Simons-Sullivan K-theory and establishes a related Grothendieck-Riemann-Roch theorem using Bismut's theorem.

Findings

Defined the Simons-Sullivan differential analytic index

Proved the differential Grothendieck-Riemann-Roch theorem in this setting

Established explicit ring isomorphisms between Freed-Lott and Simons-Sullivan theories

Abstract

We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differential K-theory using a theorem of Bismut.