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Geometry 1 (Low-Dimensional Topology) Lab
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The lab studies low-dimensional topology through braid groups and ordered groups.
AboutAbout the lab
Investigating how knots and strands are entangled, in the language of groups
This lab studies low-dimensional topology.
Its main research themes include braid groups, ordered groups, mapping class groups, and contact structures on 3-manifolds.
It investigates the properties of knots using the language of groups and classification results.
Key terms
- Braid group
- A group formed by treating the ways of braiding several strands as its elements, combined by joining braids end to end
- Low-dimensional topology
- A field that studies 3- and 4-dimensional shapes and knots through properties that do not change under stretching and shrinking
- Fibered knot
- A knot whose complement splits neatly into surfaces arranged over a circle
ResearchResearch themes
The lab studies braid groups, low-dimensional topology, and ordered groups. Contact structures on 3-manifolds and mapping class groups are also among its research themes.
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MembersFaculty
- ProfessorTetsuya Ito
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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: “Hopf Link” Jim.belk / Public domain (cropped)
- The 3-Dimensional Clasp Number of Knots: “Blue Trefoil Knot” Jim.belk / Public domain (cropped)
- Related lab (Geometry 1 (Low-Dimensional Topology, Gauge Theory) Lab): “Superfície não orientável - Bordo trifólio” Object made by MockUp Company, photo by Rodrigo.Argenton / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics (Topological Data Analysis) Lab (Yasuaki Hiraoka)): “Persistence Diagram” Rrrlw / CC BY-SA 4.0 (cropped)
- Related lab (Geometry 1 Lab (Topology; Tadayuki Watanabe)): “Borromean Rings Illusion” Jim.belk / Public domain (cropped)
- Related lab (Algebra 2 (Algebraic Geometry) Lab (Osamu Fujino)): “Sarti's octic with 144 nodes” Salix alba / CC BY-SA 4.0 (cropped)
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