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Hirose Lab
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A lab that explores low-dimensional topology through the mapping class groups of manifolds.
AboutAbout the lab
Approaching the mysteries of low-dimensional manifolds
The Hirose Lab studies shapes called manifolds in the field of low-dimensional topology.
Roughly speaking, a manifold is a shape that can be regarded locally as Euclidean space.
Many mysteries still remain about manifolds of low dimensions, such as three and four dimensions.
The lab conducts its research by relating it to concrete subjects such as mapping class groups and knots.
Key terms
- Manifold
- A shape that can be regarded locally as Euclidean space. One of the central objects of geometry in mathematics.
- Mapping class group
- A group formed from the deformations that map a shape such as a surface onto itself, where deformations that can be continuously moved onto one another are regarded as the same.
- Knot
- A loop of string placed in space. A concrete object that is studied in relation to manifolds.
ResearchResearch themes
The lab aims to elucidate the geometric structure of low-dimensional manifolds. It studies low-dimensional manifolds in relation to concrete subjects such as mapping class groups and knots.
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MembersFaculty
- ProfessorSusumu Hirose
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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: “Tesseract torus” WatchduckYou can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck". / CC BY 4.0 (cropped)
- Mapping Class Groups of Low-Dimensional Manifolds: “Surface generated by transformation (rotation + scaling) of a segment” Nunzio Dimola / CC BY-SA 4.0 (cropped)
- Related lab (田中研究室): “Poincare Group Commutation Structure” Travisrm89 / CC0 (cropped)
- Related lab (馬場研究室): “Sarti surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Related lab (江崎研究室): “WienerSausage” R.e.b. / Public domain (cropped)
- Related lab (伊藤・呼子研究室): “Würfel” Dietmar Rabich / CC BY-SA 4.0 (cropped)
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