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Sakasai Lab
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A topology lab that explores 3-manifolds through the mapping class groups of surfaces.
AboutAbout the lab
Studying space through the symmetries of surfaces
The Sakasai Lab studies mapping class groups of surfaces from the perspective of topology.
The mapping class group is the group of isotopy classes of self-diffeomorphisms of a surface. It appears not only in topology and differential geometry but also in many other areas of mathematics, such as algebra and mathematical physics.
The lab aims to elucidate the structure of cohomology rings through the structure of these groups and the topology of moduli spaces. Recently, it has been investigating the structure of related infinite-dimensional Lie algebras through both theoretical analysis and computer experiments.
Using the homology cobordism group of surfaces as a starting point, the lab also works on constructing new invariants of knots and 3-manifolds.
Key terms
- Mapping class group
- The group formed by grouping together the transformations of a surface that can be turned into one another by continuous deformation
- 3-manifold
- A shape that, near every point, looks the same as the 3-dimensional space we live in
- Invariant
- A quantity that does not change when a shape is deformed. It serves as a clue for telling whether two shapes are the same or different
ResearchResearch themes
The lab studies, from the perspective of topology, mapping class groups of surfaces and automorphism groups of free groups. It aims to understand the structure of these groups and the topological properties of moduli spaces, and to apply this understanding to the theory of 3-manifolds.
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MembersFaculty
- Associate ProfessorTakuya SakasaiPublications ↗
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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: “Triple torus illustration” Oleg Alexandrov / Public domain (cropped)
- Structure and Applications of Mapping Class Groups: “Curves on surface of genus 2” Café Bene / CC BY-SA 3.0 (cropped)
- Related lab (Habiro Lab): “3D Borromean Rings” Jim.belk / Public domain (cropped)
- Related lab (Asuke Lab): “Reeb foliation half-torus POV-Ray” Ilya Voyager / CC0 (cropped)
- Related lab (Ueda Lab): “Quintic 1” The original uploader was Floriang at German Wikipedia. / CC BY-SA 3.0 (cropped)
- Related lab (Konno Lab): “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
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