Relative Chern character, boundaries and index formulas

Pierre Albin, Richard Melrose

Research output: Contribution to journalArticlepeer-review


For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have "geometric K-theory", namely the "transmission algebra" introduced by Boutet de Monvel [5], the "zero algebra" introduced by Mazzeo in [9, 10] and the "scattering algebra" from [16], we give explicit formulas for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fiber operators. This involves appropriate descriptions, in each case, of the cohomology with compact supports in the interior of the total space of a vector bundle over a manifold with boundary in which the Chern character, mapping from the corresponding realization of K-theory, naturally takes values.

Original languageEnglish (US)
Pages (from-to)207-250
Number of pages44
JournalJournal of Topology and Analysis
Issue number3
StatePublished - Sep 2009
Externally publishedYes


  • Atiyah-Bott index theorem
  • Atiyah-Singer index theorem
  • Boutet de Monvel index theorem
  • Chern character
  • boundary value problems
  • scattering calculus
  • smooth K-theory
  • zero calculus

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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