Konferenz: Swiss-Russian Seminar on Moduli Spaces and Physics


A Riemann-Roch formula for holomorphic differential operators

{{_Ltalk:R}} Prof. Dr. Giovanni Felder
Datum: 05.12.07   Zeit: 10.30 - 11.30   Raum: Y27H36

Abstract: The Lefschetz number of a holomorphic differential operator acting on sections of a vector bundle on a compact complex manifold is the alternating sum of traces of the induced map on cohomology. The Feigin-Shoikhet conjecture (now a theorem) expresses the Lefschetz number of an operator D as the integral over the manifold of a differential form depending locally on D and on a chosen connection. When D is the identity, the formula reduces to the Riemann-Roch-Hirzebruch formula, with the Chern-Weil representative of the characteristic class. In the case of a compact group action there are localization formulae expressing the Lefschetz number as an integral over fixed point sets. This talk is based on joint papers with B. Feigin and B. Shoikhet, with M. Engeli and with X. Tang.