Indices of Toeplitz tuples on pseudoregular domains
【摘要】：正 This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tuple T n is ( -1)n time wrapping number of 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 that C* (Ω) ≌ C* ( Bn) for every Poincare domain Ω in Cn( n≠2). It is also noticed that C* (Ω) ≌ C* ( B2) if and only if the Poincaré conjecture is true for Ω.