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Geometry 1 Lab (Topology; Tadayuki Watanabe)
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The lab studies topology through diffeomorphism groups and knot invariants.
AboutAbout the lab
Investigating the spaces formed by deformations of shapes through topology.
The lab studies diffeomorphism groups and spaces of embeddings in the field of topology.
Finite type invariants of 3-manifolds and knots are also among its research themes.
Through collaborative research, it works on distinguishing families of deformations of shapes using invariants constructed from graphs.
Key terms
- Diffeomorphism group
- The group of all maps that deform a shape smoothly and reversibly
- Finite type invariant
- Among the quantities that distinguish knots and 3-manifolds, one that is determined at some finite stage
- Embedding
- Placing one shape inside another without any overlap
ResearchResearch themes
The lab studies the topology of diffeomorphism groups and spaces of embeddings, as well as finite type invariants of 3-manifolds and knots.
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MembersFaculty
- ProfessorTadayuki Watanabe
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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: “Borromean Rings Illusion” Jim.belk / Public domain (cropped)
- Topology of Diffeomorphism Groups: “Brunnian-3-not-Borromean” AnonMoos / Public domain (cropped)
- Related lab (Algebra 2 and Geometry 2 Lab (Complex Geometry, Algebraic Geometry, Differential Geometry; Kenichi Yoshikawa)): “Espace de Calabi-Yau” Rogilbert / Public domain (cropped)
- Related lab (Geometry 1 and Analysis 2 (Topology, Operator Algebras) Lab (Kubota)): “Topological insulator band structure” A13ean / CC BY-SA 4.0 (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)
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