A subgroup theorem for homological filling functions
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Abstract
We use algebraic techniques to study homological lling functions of groups and their subgroups. If G is a group admitting a nite .n C 1/-dimensional K.G; 1/ and H G is of type F nC1 , then the n th homological lling function of H is bounded above by that of G. This contrasts with known examples where such inequality does not hold under weaker conditions on the ambient group G or the subgroup H . We include applications to hyperbolic groups and homotopical lling functions.
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