| EPSRC Reference: |
EP/Y022939/1 |
| Title: |
Searching for slice-ribbon counterexamples |
| Principal Investigator: |
Owens, Dr B |
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| Department: |
School of Mathematics & Statistics |
| Organisation: |
University of Glasgow |
| Scheme: |
Standard Research - NR1 |
| Starts: |
18 October 2023 |
Ends: |
17 August 2024 |
Value (£): |
81,984
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
Primitive people are said to have believed that the world was flat. This was a reasonable assumption based on local data. Low-dimensional topologists study 3- and 4-dimensional spaces known as manifolds in order to understand the possible geometry and topology of the physical universe and spacetime that we inhabit. For the purposes of this project, a knot is a smooth closed curve --- a loop --- in 3-dimensional space. Knots are fundamental objects which appear in many areas of science. In particular they are the building blocks for low-dimensional topology: every 3- or 4-dimensional manifold can be described using a Kirby diagram involving one or more knots. Understanding surfaces in 4-dimensional space whose boundary is a given knot is also fundamental for 4-dimensional topology, and is closely related to the study of line fields in nature such as magnetic field lines and fluid vortices.
This ambitious project will develop, and implement in a computer program, a new approach to producing knotted 2-dimensional spheres in 4-dimensional space, and slices of those 2-spheres which are knotted circles in 3-dimensional space which bound 2-dimensional disks in 4-space. A longstanding conjecture due to Fox predicts that such slice knots in fact bound a special kind of disk called a ribbon disk which can be seen in 3-dimensional space. Our aim is to settle this conjecture by finding a slice knot which cannot bound a ribbon disk.
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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 |
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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.gla.ac.uk |