English

Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics

Quantum Algebra 2007-05-23 v1 High Energy Physics - Theory Differential Geometry

Abstract

In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-Roch-Hirzebruch 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 operations can "produce" the integral in some set-up, has an independent from the RRH theorem interest. We finish the paper by some open questions arising when the main construction is applied to the cyclic homology (instead of the Hochschild homology).

Keywords

Cite

@article{arxiv.math/0401400,
  title  = {Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics},
  author = {Boris Feigin and Andrey Losev and Boris Shoikhet},
  journal= {arXiv preprint arXiv:math/0401400},
  year   = {2007}
}

Comments

24 pages, no figures, LaTeX