Combinatorial Extension Cohomology I. Groups

ISSN： 0001-8708

Source： Advances in Mathematics, Vol.106, Iss.1, 1994-06, pp. : 96-117

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Abstract

A new method is proposed for calculating the measurable, continuous, or differentiable cohomology of a group extension, which involves deriving functional equations for the restrictions of cocycles to certain well-behaved subsets of its domain and showing that the cocycle can be written as a certain sum of such restrictions. This technique is capable of determining how the quotients of the filtration given by the spectral sequence fit together, and is applied to the case of the Heisenberg group H_n to yield extremely explicit cocycle representatives, culminating in a stability theorem regarding multilinearizability of cocycles. One of the main tools for doing this is the derivation of a formula for trivializing the product of two alternating multilinear functions, one of which is the nondegenerate bilinear one defining the Heisenberg group, which has interesting connections with Hodge theory.