| EPSRC Reference: |
GR/S97095/01 |
| Title: |
Covering spaces of 3-manifolds and the geometric theory of finite index subgroups |
| Principal Investigator: |
Lackenby, Professor M |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Advanced Fellowship (Pre-FEC) |
| Starts: |
01 October 2004 |
Ends: |
30 September 2009 |
Value (£): |
245,517
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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22 Apr 2004
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Mathematics Advanced Fellowships Interview panel
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Deferred
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12 Mar 2004
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Maths Fellowships Sifting Panel 2004
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Deferred
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Summary on Grant Application Form |
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A `manifold' is a mathematical object that, near any point, looks like ordinary Euclidean space, but globally n not. A familiar example is the surface of the Earth, which only locally looks like a plane. Another key example is universe which, according to general relativity, is not flat: it is a manifold. Manifolds play a central role in mathema and theoretical physics. The aim of much current research is to describe their possible topology (i.e. their shape) ; geometry (i.e. their intrinsic notion of distance). Three-dimensional manifolds are the focus of intense research z worldwide level, and it is these that I study. It is an interesting fact that their theory is qualitatively different from tha higher-dimensional manifolds. They are closely linked to the theory of groups, which are algebraic structures that desci the language of symmetry. This is because, associated with any manifold, there is a group (its `fundamental group'), wl strongly controls its topology, particularly in dimension three. I intend to explore and develop the interaction betty three-dimensional manifolds and groups. Many key unsolved problems relate to the possible subgroups of the fundame: group of a three-dimensional manifold, and it is these that I hope to resolve. This will contribute to the UK's strengtl an important area of research. I will be based in the Mathematical Institute at the University of Oxford, working as 1 of active research groups in geometry, topology and algebra.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |