%0 DATA
%A Ahsan Ahmed, Jaleel
%D 2017
%T Constructing free resolutions of cohomology algebras
%U https://monash.figshare.com/articles/Constructing_free_resolutions_of_cohomology_algebras/4719793
%R 10.4225/03/58b8c5768d48f
%2 https://ndownloader.figshare.com/files/7706329
%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.