Some index formulae on the moduli space of stable parabolic vector bundles

Pierre Albin, Frédéric Rochon

Research output: Contribution to journalArticlepeer-review

Abstract

We study natural families of ℓ-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulae for the Chern classes of the associated determinant bundles consistent with a result of Takhtajan and Zograf.

Original languageEnglish (US)
Pages (from-to)1-37
Number of pages37
JournalJournal of the Australian Mathematical Society
Volume94
Issue number1
DOIs
StatePublished - Feb 2013

Keywords

  • cusps
  • index formula
  • parabolic bundles

ASJC Scopus subject areas

  • Mathematics(all)

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