Vanishing and non-vanishing for the first $L^p$-cohomology of groups
نویسندگان
چکیده
منابع مشابه
Non-vanishing on the first cohomology
— It is shown here that, for any finitely generated lattice r in certain semi simple groups over local fields of positive characteristics, H (r. Ad) is nonvanishing; this is in sharp contrast with the situation in characteristic zero. Let Kbe a local field (i. e. a non-discrete locally compact field), and let G be a connected semi simple algebraic group defined over K. Let G = G (K), and let r ...
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Let Γ be an arithmetic subgroup of G = SL(n,R), with n > 2. (More generally, Γ could be any irreducible arithmetic subgroup of any semisimple Lie group of higher real rank.) We will describe a proof (due to Margulis) that the first cohomology of Γ vanishes (with coefficients in any finite-dimensional real representation). The result is a consequence of the much stronger statement, known as the ...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2005
ISSN: 0010-2571
DOI: 10.4171/cmh/18