Indices of Toeplitz tuples on pseudoregular domains

Abstract

This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tupleT n is (-1) n time wrapping number of φ n around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincare domain. As another application, it is shown thatC*(Ω)≅C*(Bn) for every Poincare domain Ω inC n (n≠2). It is also noticed thatC*(Ω)≅C*(B 2) if and only if the Poincare conjecture is true for ∂Ω.