Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729646 |
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Title: | The cohomology of free loop spaces of homogeneous spaces | ||||||
Author: | Burfitt, Matthew Ingram |
ISNI:
0000 0004 6496 2508
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Awarding Body: | University of Southampton | ||||||
Current Institution: | University of Southampton | ||||||
Date of Award: | 2017 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
The free loops space ΛX of a space X has become an important object of study particularly in the case when X is a manifold. The study of free loop spaces is motivated in particular by two main examples. The first is their relation to geometrically distinct periodic geodesics on a manifold, originally studied by Gromoll and Meyer in 1969. More recently the study of string topology and in particular the Chas-Sullivan loop product has been an active area of research. A complete flag manifold is the quotient of a Lie group by its maximal torus and is one of the nicer examples of a homogeneous space. Both the cohomology and Chas-Sullivan product structure are understood for spaces Sn, CPn and most simple Lie groups. Hence studying the topology of the free loops space on homogeneous space is a natural next step. In the thesis we compute the differentials in the integral Leray-Serre spectral sequence associated to the free loops space fibrations in the cases of SU(n+1)/Tn and Sp(n)/Tn. Study in detail the structure of the third page of the spectral sequence in the case of SU(n) and give the module structure of H*(Λ(SU(3)/T2);Z) and H*(Λ(Sp(2)/T2);Z).
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Supervisor: | Grbic, Jelena | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.729646 | DOI: | Not available | ||||
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