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Topology and Singularity Theory Lab
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A topology lab that studies the shape of manifolds through the singularities of maps.
AboutAbout the lab
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The lab studies topology, investigating the overall shape of manifolds, which are geometric objects, by using the singularities of differentiable maps defined on them as clues.
By restricting the types of singularities to simple ones, or focusing on low-dimensional cases, the lab investigates how singularities relate to the structure of manifolds.
The lab also works broadly across many areas of topology, including knots, 4-manifolds, and isolated singularities of complex hypersurfaces.
It also works on applications of topology, such as the visual analysis of DNA knots and multivalued function data, and is interested in studying the properties of matter and materials from a topological viewpoint.
Key terms
- manifold
- A generalization of shapes such as curves and surfaces, in which the neighborhood of every point looks like ordinary space
- differentiable map
- A smooth map that can be differentiated. It describes a correspondence from one manifold to another manifold or space
- singularity
- A point where the behavior of a map becomes special. Singularities appear around points of a manifold
NewsLab news
View More ↗ResearchResearch themes
It has long been known that differentiable functions on a manifold are useful for studying its global structure. This lab studies the relationship between the singularities of differentiable maps between manifolds and the structure of the manifolds.
*Illustrative imageGlobal singularity theory of differentiable maps
The lab studies how the singularities of differentiable maps between manifolds relate to the structure of the manifolds. The research restricts the types of singularities to simple ones, or focuses on low-dimensional cases.
*Illustrative imageA broad range of topology and its applications
The lab studies many areas of topology, including isolated singularities of complex hypersurfaces, fibered knots, 4-manifolds, and the unknotting number. It also works on applications to other fields, such as the visual analysis of DNA knots and multivalued function data.
MembersFaculty
- ProfessorOsamu Saeki
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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: “Bastard Weaver s Knot diagram-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Global singularity theory of differentiable maps: “Paper-airplane-v-shape-tail” Manhdeptraipro2114 / CC BY 4.0 (cropped)
- A broad range of topology and its applications: “Klein Bottle Parametrized Symmetric Half” AugPi / CC BY-SA 4.0 (cropped)
- Related lab (Topology and Singularity Theory Lab): “Linkedin maps data visualization” Luc Legay / CC BY-SA 4.0 (cropped)
- Related lab (Applied Algebra and Mathematical Crystallography Lab): “Simple Cubic Lattice (Brillouin zone)” Auro69 at en.wikipedia / Public domain (cropped)
- Related lab (Applied Algebra and Mathematical Crystallography Lab): “Rendering of quasicrystal structure” LinKayser / CC BY-SA 4.0 (cropped)
- Related lab (Probability Theory and Random Point Processes Lab): “A boolean model” Tensorproduct / CC BY-SA 4.0 (cropped)
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