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Topology Lab
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Knot theory, which examines how tangled a piece of string is using numbers and polynomials.
AboutAbout the lab
Untangling strings with geometry.
Prof. Kawamura studies knot theory and low-dimensional topology.
Put simply, knot theory is a branch of geometry that examines how tangled a piece of string is.
The professor studies the properties of invariants of knots and links, that is, numbers, polynomials, and the like that express their complexity.
The professor reportedly never stops being amazed by the depth of the field: results from advanced theories such as gauge theory, which developed in physics, are applied to proving formulas that look simple at first glance.
Key terms
- Link
- Several closed loops of string tangled together. With just one loop, it is called a knot
- Invariant
- A number, polynomial, or similar quantity that expresses the complexity of a knot or link
- Low-dimensional topology
- A branch of geometry that studies the shape and connectivity of low-dimensional figures and spaces
ResearchResearch themes
The lab studies knot theory, which examines how tangled a piece of string is, and low-dimensional topology. It investigates the properties of invariants, which express the complexity of knots and links using numbers, polynomials, and the like.
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MembersFaculty
- Associate ProfessorTomomi Kawamura
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “TrefoilKnotOrder2Symmetry” Wstomv / CC BY-SA 4.0 (cropped)
- Knot invariants and how to untie knots: “Figure-Eight Knot diagram” Wstomv / CC BY 4.0 (cropped)
- Related lab (Topology and Differential Geometry Lab): “Schwarz P Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (Ishii Lab): “Surface of degree 7” Jean Constant / CC BY-SA 4.0 (cropped)
- Related lab (Algebraic Number Theory, Arithmetic Geometry, and Algebraic Geometry Lab): “Clay tablet, mathematical, geometric-algebraic, similar to the Euclidean geometry. From Tell Harmal, Iraq. BCE. Iraq Museum” Osama Shukir Muhammed Amin FRCP(Glasg) / CC BY-SA 4.0 (cropped)
- Related lab (Probability Theory and Information Theory Lab): “Telecommunications equipment adjacent to The Three Sisters” Schwede66 / CC BY-SA 4.0 (cropped)
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