| EPSRC Reference: |
GR/T28805/01 |
| Title: |
Symmetric Powers of Spheres |
| Principal Investigator: |
Strickland, Professor N |
| Other Investigators: |
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| Department: |
Mathematics and Statistics |
| Organisation: |
University of Sheffield |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 July 2005 |
Ends: |
30 June 2008 |
Value (£): |
135,981
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Algebraic topology is the study of abstract spaces, usually with many more than three dimensions. A mathematical problem involving n independent variables can naturally be formulated in terms of an abstract n-dimensional space, which exists independently of the three-dimensional physical space in which we live. Topologists study how spaces are built up from simpler pieces, what holes they have in them and how the holes link together or twist around each other, and so on. Many interesting spaces are defined combinatorially: one starts with simple shapes like triangles or pyramids, and glues them together according to some system of rules, and the topology of the resulting space has an interesting relationship with the structure of the rules. Topologists also use various methods (called generalised cohomology theories ) to relate topological problems about spaces to easier questions in abstract algebra. This project will use a particular generalised cohomology theory (called Morava E-theory ) to study a number of different spaces that have been found to be important in other parts of topology. Some of the relevant spaces are defined in terms of the combinatorics of sets and their partitions into smaller subsets. Others are defined in more complicated ways, making contact with a wide range of ideas in other fields of mathematics.
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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.shef.ac.uk |