An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds

Supersymmetric Proof of the Hirzebruch– Riemann–Roch Theorem for Non-Kähler Manifolds

We present the proof of the HRR theorem for a generic complex compact manifold by evaluating the functional integral for the Witten index of the appropriate supersymmetric quantum mechanical system.

Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics

In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-RochHirzebruch formula for an arbitrary differential operator. Instead of the Grothendieck-Sato isomorphism, we use the Topological Quantum Mechanics (more or less equivalent to the well-known constructions with the Massey operations from [KS], [P], [Me]). The statement that the Massey op...

A Riemann–roch–hirzebruch Formula for Traces of Differential Operators

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator...

Riemann-roch Theorems for Differentiable Manifolds

Integral Grothendieck-riemann-roch Theorem

in the Chow ring with rational coefficients CH(S)Q = ⊕nCH (S)Q. Here ch is the Chern character and Td(TX), Td(TS) stand for the Todd power series evaluated at the Chern classes of the tangent bundle of X, respectively S. Since both sides of (1.1) take values in CH(S)Q := CH (S)⊗Q, only information modulo torsion about the Chern classes of f∗[F ] can be obtained from this identity. The goal of o...