EPSRC Reference: 
EP/Y022939/1 
Title: 
Searching for sliceribbon counterexamples 
Principal Investigator: 
Owens, Dr B 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
School of Mathematics & Statistics 
Organisation: 
University of Glasgow 
Scheme: 
Standard Research  NR1 
Starts: 
18 October 2023 
Ends: 
17 August 2024 
Value (£): 
81,984

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

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. Lowdimensional topologists study 3 and 4dimensional 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 3dimensional space. Knots are fundamental objects which appear in many areas of science. In particular they are the building blocks for lowdimensional topology: every 3 or 4dimensional manifold can be described using a Kirby diagram involving one or more knots. Understanding surfaces in 4dimensional space whose boundary is a given knot is also fundamental for 4dimensional 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 2dimensional spheres in 4dimensional space, and slices of those 2spheres which are knotted circles in 3dimensional space which bound 2dimensional disks in 4space. 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 3dimensional space. Our aim is to settle this conjecture by finding a slice knot which cannot bound a ribbon disk.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.gla.ac.uk 