The Arveson-Douglas Conjecture studies submodules and quotient modules of analytic function spaces arising from ideals or complex varieties. Given the essential commutativity of the module actions on such quotient modules, that is, given the conjecture holds, these modules define K-homology elements on the associated variety. On the other hand, the Helton-Howe's formula on traces of anti-symmetric sums gives another possible geometric invariant on such modules. This requires some finer commutativity than the Arveson-Douglas Conjecture. In this talk, I will give an introduction to the above topics and discuss about possible future developments.