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arXiv · 2301.09118

Cocycles de groupe pour GL$_n$ et arrangements d'hyperplans

Nicolas Bergeron·Pierre Charollois·Luis Garcia
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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.''

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Nicolas Bergeron, Pierre Charollois, Luis Garcia. 2023-01-22. Cocycles de groupe pour GL$_n$ et arrangements d'hyperplans. https://arxiv.org/abs/2301.09118

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