10.4225/03/58b8c5768d48f Jaleel, Ahsan Ahmed Ahsan Ahmed Jaleel Constructing free resolutions of cohomology algebras Monash University 2017 1959.1/1232059 Cohomology algebras thesis(doctorate) Integral cohomology opertation H(R)-algebra Bousfield cohomology spectral sequence monash:163852 Open access 2016 Cosimplicial resolution ethesis-20160113-152311 2017-03-03 01:23:00 Thesis https://bridges.monash.edu/articles/thesis/Constructing_free_resolutions_of_cohomology_algebras/4719793 The H(R)-algebra of a space is defined as the algebraic object consisting of the graded cohomology groups of the space with coefficients in a general ring R, together with all primary cohomology operations on these groups, subject to the relations between the operations.This structure can be encoded as a functor from the category H(R) containing products of Eilenberg-Mac Lane spaces over R to the category of pointed sets. The free H(R)-algebras are the H(R)-algebras of a product of Eilenberg-Mac Lane spaces. In this thesis we show how to construct free simplicial resolutions of H(R)-algebras using the free and underlying functors. Given a space X, we also construct a cosimplicial space such that the cohomology of this cosimplicial space is a free simplicial resolution of the H(R)-algebra of X. For R = Fp, the finite field on p elements, this cosimplicial resolution fits the E2 page of a spectral sequence and give convergence results under certain finiteness restrictions on X. For R = Z, the integers, a similar result is not obtained and the reasons for this are given.