Resumen de Expression de la différentielle d3 de la suite spectrale de Hochschild-Serre en cohomologie bornée réelle
For discrete groups, we construct two bounded cohomology classes with coefficients in the second space of the reduced real .1-homology. Precisely, we associate to any discrete group G a bounded cohomology class of degree two noted g2 2 H2 b (G,H .1 2 (G,R)). For G and �® groups and �Æ : �® ! Out(C) any homomorphism we associate a bounded cohomology class of degree three noted [�Æ] 2 H3 b (�®,H .1 2 (G,R)). When the outer homomorphism �Æ : �® ! Out(C) induces an extension of G by �® we show that the class g2 is �®-invariant and that the differential d3 of Hochschild-Serre spectral sequence sends the class g2 on the class [�Æ] :
d3(g2) = [�Æ]. Moreover, we show that for any integer n 0 the differential d3 : En,2 3 ! En+3,0 3 of Hochschild-Serre spectral sequence in real bounded cohomology is given as a cup-product by the class [�Æ].
