A Note on Cohomological Vanishing and the Linear Isoperimetric Inequality
نویسنده
چکیده
If G is a finitely presented group, then H2 (∞) (G,A) vanishes for all injective Banach spaces iff the regularized homological area function satisfies the linear isoperimetric inequality. This contrasts with the known result that G is word hyperbolic iff the homological area function satisfies the linear isoperimetric inequality. A closed 3-manifold group G is hyperbolic iff H2 (∞) (G,A) vanishes for all injective Banach spaces A. A vanishing theorem is proved for the fundamental group of a closed Riemannian manifold of negative curvature. §
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