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Type: Theses
Title: Topics in equivariant cohomology
Author: Keating Hughes, Luke
Issue Date: 2017
School/Discipline: School of Mathematical Sciences
Abstract: The equivariant cohomology of a manifold M acted upon by a compact Lie group G is defined to be the singular cohomology groups of the topological space (M × EG)/G. It is well known that the equivariant cohomology of M is parametrised by the Cartan model of equivariant differential forms. However, this model has no obvious geometric interpretation – partly because the expression above is not a manifold in general. Work in the 70s by Segal, Bott and Dupont indicated that this space can be constructed as the geometric realisation of a simplicial manifold that is naturally built out of M and G. This simplicial manifold carries a complex of so-called simplicial differential forms which gives a much more natural geometric interpretation of differential forms on the topological space (M × EG)/G. This thesis provides a model for the equivariant cohomology of a manifold in terms of this complex of simplicial differential forms. Explicit chain maps are constructed, inducing isomorphisms on cohomology, between this complex of simplicial differential forms and the more standard models of equivariant cohomology, namely the Cartan and Weil models.
Advisor: Stevenson, Daniel
Murray, Michael Kevin
Dissertation Note: Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2017.
Keywords: equivariant cohomology
lie groups
simplicial manifolds
Provenance: This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at:
DOI: 10.4225/55/5913cababcd11
Appears in Collections:Research Theses

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