Essentially normal Hilbert modules and Khomology Ⅲ: Homogenous quotient modules of Hardy modules on the bidisk

In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk.