1. Cocycles de groupe pour GL$_n$ et arrangements d'hyperplans
- Author
-
Bergeron, Nicolas, Charollois, Pierre, and Garcia, Luis
- Subjects
Mathematics - Number Theory ,11F75 (11F41 11F66 11F67 57R20) - Abstract
Many authors have constructed different, but related, linear group cocycles that are usually referred to as ``Eisenstein cocycles.'' The main goal of this work is to describe 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). This yields the construction of three types of ``Sczech cocycles.'', Comment: 141 pages, 3 figures, the text is in French. Submitted as a CRM Monograph
- Published
- 2023