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Homology isomorphisms between algebraic groups made discrete

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: W.G. Dwyer, S.M. Jekel, A.I. Suciu

Editorial: Bulletin of the London Mathematical Society, 25 (2), p.145-149, 1993.


Consider a split exact sequence of discrete groups $${1}to G to Gamma{underset sigma to {overset{pi} to rightleftarrows}} Gamma/G to {1}.$$ Suppose there exists a normal series $G=G_0 triangleright G_1 triangleright cdots triangleright G_n triangleright G_{n+1}={1}$, such that (1) $G_i/G_{i+1}$ is a rational vector space for $i=0, cdots, n$; (2) $G_i/G_{i+1}$ is contained in the center of $G/G_{i+1}$ for $i=0, cdots, n$; (3) there exists an element in the centre of $Gamma/G$ that induces a diagonalizable endomorphism of each $G_i/G_{i+1}$ with all eigenvalues rational and greater than 1. Then the map $pi$ induces an isomorphism $pi_*colon H_*(BGamma,Z) to H_*(B(Gamma/G),Z)$.

Cuvinte cheie: homology, lower central series, discrete groups