Geometric and Algebraic Topology
Geometric and Algebraic Topology is a research topic within Geometry and Topology. Science Explorer counts 23k research works in it since 1950. 14.5% of them reached the world's top 10% most cited for their field and year.
This cluster of papers explores the intersection of symplectic topology, knot invariants, and related areas such as holomorphic disks, Floer homology, contact geometry, group theory, hyperbolic manifolds, quantum topology, braid groups, and the study of protein knotting.
- Symplectic Topology
- Knot Invariants
- Holomorphic Disks
- Floer Homology
- Contact Geometry
- Group Theory
- Hyperbolic Manifolds
- Quantum Topology
- Braid Groups
- Protein Knotting
- Research works
- 23k fractional, since 1950
- In the world top 10%
- 3.4k per year above
- Top-10% rate
- 14.5% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- -6% the tick is no change
Which countries lead Geometric and Algebraic Topology research?
By volume, the United States and China publish the most (731 and 267 works in 2022–2025).
By volume, 2022–2025
- 1 United States 731 works
- 2 China 267 works
- 3 France 233 works
- 4 Japan 219 works
- 5 United Kingdom 191 works
- 6 Germany 189 works
- 7 Russia 176 works
- 8 India 125 works
- 9 Italy 108 works
- 10 Brazil 102 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Geometric and Algebraic Topology research?
By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Geometric and Algebraic Topology research, followed by National Research University Higher School of Economics and University of Oxford.
By volume, 2022–2025
- 1 Centre National de la Recherche ScientifiqueFrance 33 works
- 2 National Research University Higher School of EconomicsRussia 29 works
- 3 University of OxfordUnited Kingdom 28 works
- 4 Kyoto UniversityJapan 24 works
- 5 ETH ZurichSwitzerland 23 works
- 6 The Ohio State UniversityUnited States 22 works
- 7 Lomonosov Moscow State UniversityRussia 21 works
- 8 University of CambridgeUnited Kingdom 17 works
- 9 Max Planck Institute for MathematicsGermany 16 works
- 10 University of MichiganUnited States 15 works
Who are the leading researchers in Geometric and Algebraic Topology?
The most-cited researchers publishing on Geometric and Algebraic Topology include Terence Tao, A. Sarti and Shing–Tung Yau.
- 1 Terence Tao United States 3.1k citations
- 2 A. Sarti United Kingdom 2.1k citations
- 3 Shing–Tung Yau United States 2.1k citations
- 4 James A. Yorke United States 2.1k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Geometric and Algebraic Topology research done?
The largest centres of Geometric and Algebraic Topology research in 2022–2025 are Moscow (Russia), Tokyo (Japan), Paris (France) and Beijing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Guarulhos, Princeton and Bonn.
Largest cities, 2022–2025
Where it is the local speciality
- GuarulhosBR · 22.0 works69×
- PrincetonUS · 24.5 works13×
- BonnDE · 23.9 works10×
Location quotient: how much more of its research is in Geometric and Algebraic Topology than the world average.
Where is the best place to study Geometric and Algebraic Topology?
Among universities, judged by research, ETH Zurich, National Research University Higher School of Economics and Princeton University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | ETH ZurichSwitzerland | 66.8 | 14.3% | 10.8× | 23 | +51.9% |
| 2 | National Research University Higher School of EconomicsRussia | 65.3 | 9.7% | 22.3× | 29 | +149.2% |
| 3 | Princeton UniversityUnited States | 59.6 | 20.0% | 10.7× | 14 | +22.4% |
| 4 | University of OxfordUnited Kingdom | 55.6 | 12.8% | 7.2× | 28 | +2.7% |
| 5 | Kyoto UniversityJapan | 51.8 | 6.9% | 10.3× | 24 | +0.4% |
| 6 | Rice UniversityUnited States | 50.9 | 14.8% | 14.3× | 10 | +57.0% |
| 7 | University of WarwickUnited Kingdom | 50.8 | 11.4% | 10.4× | 15 | -19.7% |
| 8 | Stony Brook UniversityUnited States | 50.6 | 13.7% | 12.9× | 12 | +33.2% |
| 9 | Université Grenoble AlpesFrance | 49.4 | 19.0% | 8.7× | 9 | +21.7% |
| 10 | Université Paris-SaclayFrance | 49.3 | 6.5% | 8.2× | 10 | +190.9% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Geometric and Algebraic Topology research growing?
Output in 2018–2022 was 6% lower than in 2013–2017, peaking in 2025. The fastest-growing topics are Geometric and Algebraic Topology.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.