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# Constructing free resolutions of cohomology algebras

thesis

posted on 2017-03-03, 01:23 authored by Jaleel, Ahsan AhmedThe 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.

## History

## Campus location

Australia## Principal supervisor

Andrew Percy## Year of Award

2016## Department, School or Centre

School of Applied Sciences and Engineering (Gippsland)## Degree Type

DOCTORATE## Faculty

Faculty of Science## Usage metrics

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