4719793_monash_163852.pdf (962.93 kB)
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
AustraliaPrincipal supervisor
Andrew PercyYear of Award
2016Department, School or Centre
School of Applied Sciences and Engineering (Gippsland)Degree Type
DOCTORATEFaculty
Faculty of ScienceUsage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC