Isoperimetric inequalities and the Friedlander-Milnor conjecture
Abstract
Description
We prove that Friedlander's generalized isomorphism conjecture on the cohomology of algebraic groups, and hence the Isomorphism Conjecture for the cohomology of the complex algebraic Lie group G(C) made discrete, are equivalent to the existence of an isoperimetric inequality in the homological bar complex of G(F), where F is the algebraic closure of a finite field.
20 pages, revised. At the referee's request, historically inappropriate uses of the term "Milnor's conjecture" replaced by "Friedlander's conjecture". Information added on the history of the conjecture(s). Two references added. No mathematical changes. To appear in Crelle's Journal
20 pages, revised. At the referee's request, historically inappropriate uses of the term "Milnor's conjecture" replaced by "Friedlander's conjecture". Information added on the history of the conjecture(s). Two references added. No mathematical changes. To appear in Crelle's Journal