%0 Thesis %A Jaleel, Ahsan Ahmed %D 2017 %T Constructing free resolutions of cohomology algebras %U https://bridges.monash.edu/articles/thesis/Constructing_free_resolutions_of_cohomology_algebras/4719793 %R 10.4225/03/58b8c5768d48f %2 https://bridges.monash.edu/ndownloader/files/16416650 %K 1959.1/1232059 %K Cohomology algebras %K thesis(doctorate) %K Integral cohomology opertation %K H(R)-algebra %K Bousfield cohomology spectral sequence %K monash:163852 %K Open access %K 2016 %K Cosimplicial resolution %K ethesis-20160113-152311 %X 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. %I Monash University