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Type: Artigo de periódico
Title: A note on projective and flat dimensions and the Bieri-Neumann-Strebel-Renz Sigma-invariants
Author: Kochloukova, DH
Abstract: Let G he a finitely generated group, and A a Z [G]-module of flat dimension n such that the homological invariant Sigma(n)(G, A) is not empty. We show that A has projective dimension n as a Z[G]-module. In particular, if G is a group of homological dimension hd(G) = n such that the homological invariant Sigma(n)(G, Z) is not empty, then G has cohomological dimension cd(G) = n. We show that if G is a finitely generated soluble group, the converse is true subject to taking a subgroup of finite index, i.e., the equality cd(G) = hd(G) implies that there is a subgroup H of finite index in G such that Sigma(infinity)(H, Z) not equal 0.
Subject: cohomological dimension
flat dimension
Country: EUA
Editor: Taylor & Francis Inc
Rights: fechado
Identifier DOI: 10.1080/00927870601041706
Date Issue: 2007
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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