Projectively Invariant Cocycles of Holomorphic Vector Fields on an Open Riemann Surface

Bouarroudj Sofiane, Gargoubi Hichem

Research output: Contribution to journalArticle

Abstract

Let Σ be an open Riemann surface and Hol(Σ) be the Lie algebra of holomorphic vector fields on Σ. We fix a projective structure (i.e. a local SL2(C)-structure) on Σ. We calculate the first group of cohomology of Hol(Σ) with coefficients in the space of linear holomorphic operators acting on tensor densities, vanishing on the Lie algebra sl2(C). The result is independent on the choice of the projective structure. We give explicit formulas of 1-cocycles generating this cohomology group.

Original languageEnglish (US)
Pages (from-to)33-40
Number of pages8
JournalTokyo Journal of Mathematics
Volume25
Issue number1
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)

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