Sczech cocycles and hyperplane arrangements 2

Abstract: Many authors, among which Nori, Sczech, Solomon, Stevens, or more recently Beilinson—Kings—Levin and Charollois—Dasgupta—Greenberg, have constructed different, but related, linear groups cocycles that are usually referred to as « Eisenstein cocycles. » In these series of lectures I will explain a topological construction that is a common source for all these cocycles. One interesting feature of this construction is that starting from a purely topological class it leads to the algebraic world of meromorphic forms on hyperplane complements in n-fold products of either the (complex) additive group, the multiplicative group or a (family of) elliptic curve(s). We will see that eventually our construction reveals hidden relations between products of elementary (rational, trigonometric or elliptic) functions) governed by relations between classes in the homology of linear groups. This is based on a work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh

Mathematics

Audience: researchers in the topic

CRM workshop: Arithmetic quotients of locally symmetric spaces and their cohomology

Series comments: Zoom registration: umontreal.zoom.us/meeting/register/tJwkfu6vpzItHtPb49yDLrPlCtLyb5kvjuYP