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...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.展开更多
基金Projects(51675092,51775099)supported by the National Natural Science Foundation of ChinaProjects(E2018501030,E2018501033,E2018501032)supported by the Natural Science Foundation of Hebei Province,China.
基金financial supports from the National Natural Science Foundation of China(Nos.51675092,51775099)the Natural Science Foundation of Hebei Province,China(Nos.E2018501032,E2018501033)。
文摘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.