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Geometry 1 (Topology) Lab (Shigeru Takamura)
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The lab studies manifolds through finite group actions and quotient families.
AboutAbout the lab
Classifying symmetric shapes as families.
The Takamura Lab studies manifolds with finite group actions in the field of topology.
The lab has introduced fibrations called "quotient families," built from linear representations of finite groups, and works on constructing their classifying spaces, among other topics.
Degenerating families of Riemann surfaces and fractional Dehn twists are also research themes.
Key terms
- Group action
- Moving a shape in a way determined by each element of a group. It expresses symmetry
- Quotient family
- A family of shapes (a fibration) built from a linear representation of a finite group
- Riemann surface
- A surface on which functions of one complex variable are naturally defined
ResearchResearch themes
The lab studies manifolds with finite group actions and the quotient families associated with them. It is also considering higher-dimensional versions of fractional Dehn twists.
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MembersFaculty
- Associate ProfessorShigeru Takamura
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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: “Platonic solids sg01” he:משתמש:עוזי ו. / Public domain (cropped)
- Quotient families associated with regular polyhedra: “Icosahedron Petrie polygon” Carsten Steger / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 1 (Number Theory, Representation Theory) Lab): “Dedekindeta” SteJaes / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Atobe)): “Bruhat-Tits-tree-for-Q-2” 부고 / CC BY-SA 4.0 (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Kaoru Hiraga)): “KleinjCont” Empetrisor / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics (Applied Dynamical Systems, Nonlinear Analysis, Verified Numerical Computation) Lab (Tomoyuki Miyaji)): “Turing morphogen pattern resembling cheetah dappling” Philip Ball / CC BY 4.0 (cropped)
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