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http://hdl.handle.net/10662/10916
Title: | Expression de la différentielle d₃ de la suite spectrale de Hochschild-Serre cohomologie Bornée Réelle |
Authors: | Bouarich, A. |
Keywords: | Cohomology of groups;ℓ1-homology of groups;Bounded cohomology of groups;Spectral sequences;Banach spaces;Cohomología de grupos;ℓ1-homología de grupos;Cohomología limitada de grupos;Secuencias espectrales;Espacios de Banach |
Issue Date: | 2012 |
Publisher: | Universidad de Extremadura |
Abstract: | For discrete groups, we construct two bounded cohomology classes with coefficients in the second space of the reduced real ℓ₁-homology. Precisely, we associate to any discrete group G a bounded cohomology class of degree two noted g₂ ∊ H_b^² (G,(H_₂^(l₁) ) ̅ (G,ℝ)). For G and Π groups and θ : Π → Out(C) any homomorphism we associate a bounded cohomology class of degree three noted [θ] ∊ H_b^³ (Π, ,(H_₂^(l₁) ) ̅ (G,ℝ)). When the outer homomorphism θ : Π →Out(C) induces an extension of G by Π we show that the class g₂ is Π-invariant and that the differential d3 of Hochschild-Serre spectral sequence sends the class g₂ on the class [θ] :d₃(g₂) = [θ]. Moreover, we show that for any integer n ≥ 0 the differential d₃ : E_₃^(n,2)→ E_₃^(n+3,0) of Hochschild-Serre spectral sequence in real bounded cohomology is given as a cup-product by the class [θ]. |
URI: | http://hdl.handle.net/10662/10916 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 27, nº 2 (2012) |
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