Eisenstein cocycles have a long history in the literature; some of pioneers includes Sczech, Nori, and Shintani.
I constructed a version of Eisenstein cocycle (with my collaborators - Busouic, Lim, Patashnick, and Stevens) with values in a certain Milnor K-group valued distributions.
In this talk, I will outline how to construct such Eisenstein cocycle and try to compare it with various known other versions of Eisenstein cocycles (due to Sharifi-Venkatesh and Bergeron-Charollois-Garcia); I will report on some of recent progress (with Jaesung Kwon and Junyeong Park) towards this comparison.