Cohomological Lower Bounds for Isoperimetric Functions on Groups
نویسنده
چکیده
If the finitely presented group G splits over the finitely presented subgroup C, then classes are constructed in H2 (∞) (G) which reflect the splitting and which serve as lower bounds for isoperimetric functions for G. It is proved that H2 (∞) (G) = 0 for all word hyperbolic groups G. A converse is obtained for the combination theorem for hyperbolic groups of Bestvina-Feighn. The Mayer-Vietoris exact sequence for l∞-cohomology associated to a splitting of a group is established. Metabolic groups are introduced as finitely presented groups G such that H2 (∞) (G,A) = 0 for all normed abelian coefficient groups A and such groups G are shown to be characterized by possessing “thin” combings.
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