Science Explorer Interactive view Map
Subfield · Mathematics

Geometry and Topology research

Geometry and Topology is a subfield of Mathematics. Science Explorer counts 253k research works in it since 1950. 15.4% of them reached the world's top 10% most cited for their field and year.

In short: branch of mathematics at the intersection between geometry and topology.

Research works
253k
fractional, since 1950
In the world top 10%
39k
per year above
Top-10% rate
15.4%
share of its works in the world top 10%
Topics
11
Growth, 2013–17 → 2018–22
+4%
the tick is no change

What is Geometry and Topology research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Cluster Algebras, Triangulated Categories, Gromov-Witten Theory, Moduli Theory, Fixed Point Theorems, Metric Spaces. Gaining share since 2009–13: Graph Spectra, Topological Indices, Complex Analysis, Geometric Function Theory. Losing share: Geometry, Hyperbolic, Bifurcations, Planar Systems.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 22 words, with their numbers
  1. Cluster Algebras7,357◆ 1.02×1 topic
  2. Triangulated Categories7,357◆ 1.02×1 topic
  3. Gromov-Witten Theory5,072◆ 0.98×1 topic
  4. Moduli Theory5,072◆ 0.98×1 topic
  5. Fixed Point Theorems4,430◆ 1.09×1 topic
  6. Metric Spaces4,430◆ 1.09×1 topic
  7. Graph Spectra3,997▲ 1.35×1 topic
  8. Topological Indices3,997▲ 1.35×1 topic
  9. Geometry3,869▼ 0.83×1 topic
  10. Hyperbolic3,869▼ 0.83×1 topic
  11. Knot Invariants3,531◆ 0.88×1 topic
  12. Symplectic Topology3,531◆ 0.88×1 topic
  13. Bifurcations3,461▼ 0.85×1 topic
  14. Planar Systems3,461▼ 0.85×1 topic
  15. Kähler Metrics3,455◆ 1.12×1 topic
  16. Stability3,455◆ 1.12×1 topic
  17. Complex Analysis2,640▲ 1.21×1 topic
  18. Geometric Function Theory2,640▲ 1.21×1 topic
  19. Model Theory2,574◆ 0.88×1 topic
  20. Topological Dynamics2,574◆ 0.88×1 topic
  21. Geometric Morphometrics2,278◆ 0.99×1 topic
  22. Morphological Integration2,278◆ 0.99×1 topic

Which countries lead Geometry and Topology research?

On research quality in 2022–2025, the United States, China and India rank highest in Geometry and Topology. By volume, the United States and China publish the most (5.1k and 4.6k works in 2022–2025).

By research quality, 2022–2025

  1. 1 United States · #1 all time 14.3% top 10% · 5.1k works
  2. 2 China · #5 all time 14.0% top 10% · 4.6k works
  3. 3 India · #10 all time 11.3% top 10% · 2.8k works
  4. 4 United Kingdom · #3 all time 17.0% top 10% · 1.3k works
  5. 5 France · #2 all time 13.3% top 10% · 1.7k works
  6. 6 Germany · #4 all time 14.2% top 10% · 1.6k works
  7. 7 Italy · #9 all time 16.2% top 10% · 1.1k works
  8. 8 Saudi Arabia · #17 all time 20.2% top 10% · 626 works
  9. 9 Russia · #7 all time 10.3% top 10% · 1.5k works
  10. 10 Pakistan · #15 all time 26.4% top 10% · 430 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 31 countries ranked in Geometry and Topology. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Geometry and Topology

By volume, 2022–2025

  1. 1 United States 5.1k works
  2. 2 China 4.6k works
  3. 3 India 2.8k works
  4. 4 France 1.7k works
  5. 5 Germany 1.6k works
  6. 6 Russia 1.5k works
  7. 7 Japan 1.5k works
  8. 8 United Kingdom 1.3k works
  9. 9 Italy 1.1k works
  10. 10 Türkiye 949 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.

United States: 23.0%China: 21.0%India: 12.8%France: 7.7%6 others listed: 35.5%23%largest
United States5,063 · 23.0%China4,636 · 21.0%India2,819 · 12.8%France1,701 · 7.7%6 others listed7,814 · 35.5%

Shares of the rows listed above, not of the whole node.

Which institutions lead Geometry and Topology research?

University of Oxford (United Kingdom) ranks first in Geometry and Topology on research quality in 2022–2025, followed by Centre National de la Recherche Scientifique and The University of Tokyo.

By research quality, 2022–2025

  1. 1 University of Oxford United Kingdom · Oxford · #12 all time 22.2% top 10% · 138 works
  2. 2 Centre National de la Recherche Scientifique France · Paris · #6 all time 15.0% top 10% · 259 works
  3. 3 The University of Tokyo Japan · Tokyo · #16 all time 20.6% top 10% · 129 works
  4. 4 Vellore Institute of Technology University India · Vellore 32.1% top 10% · 86 works
  5. 5 Massachusetts Institute of Technology United States · Cambridge · #3 all time 23.2% top 10% · 83 works
  6. 6 Princeton University United States · Princeton · #1 all time 26.2% top 10% · 79 works
  7. 7 University of Michigan United States · Ann Arbor · #10 all time 16.6% top 10% · 95 works
  8. 8 University of Bonn Germany · Bonn · #26 all time 20.7% top 10% · 73 works
  9. 9 Lomonosov Moscow State University Russia · Moscow · #61 all time 12.2% top 10% · 156 works
  10. 10 Tsinghua University China · Beijing · #92 all time 14.7% top 10% · 119 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 56 institutions above the floor of 40 fractional works in Geometry and Topology.

Top 100 Geometry and Topology institutions

By volume, 2022–2025

  1. 1 Centre National de la Recherche Scientifique France 259 works
  2. 2 Lomonosov Moscow State University Russia 156 works
  3. 3 National Research University Higher School of Economics Russia 150 works
  4. 4 University of Oxford United Kingdom 138 works
  5. 5 The University of Tokyo Japan 129 works
  6. 6 Kyoto University Japan 127 works
  7. 7 Tsinghua University China 119 works
  8. 8 Universidad Nacional Autónoma de México Mexico 101 works
  9. 9 ETH Zurich Switzerland 97 works
  10. 10 University of Cambridge United Kingdom 97 works

Who are the leading researchers in Geometry and Topology?

Among the most productive authors in Geometry and Topology, Edward Witten, Stephan Ramon Garcia and Heng Fan rank highest on the composite score.

  1. 1 Edward Witten United States · #88 worldwide 7.2k citations · 151 works
  2. 2 Stephan Ramon Garcia United States · #107 worldwide 4k citations · 136 works
  3. 3 Heng Fan China · #132 worldwide 5.5k citations · 146 works
  4. 4 Steven J. Miller United States · #283 worldwide 3.8k citations · 110 works
  5. 5 H. S. M. Coxeter Canada · #1,398 worldwide 1.3k citations · 115 works
  6. 6 David Hilbert Germany · #2,136 worldwide 666 citations · 113 works
  7. 7 Jeffrey C. Lagarias United States · #2,191 worldwide 1.9k citations · 76 works
  8. 8 Michael Atiyah United Kingdom · #2,229 worldwide 1.4k citations · 87 works
  9. 9 Terence Tao United States · #2,469 worldwide 3.1k citations · 215 works
  10. 10 G. H. Hardy United Kingdom · #2,515 worldwide 939 citations · 96 works

Re-ranked on the composite score from the 5,018 highest-output authors in Geometry and Topology. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Geometry and Topology researchers

Where is Geometry and Topology research done?

The largest centres of Geometry and Topology research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Huairou, Bures-sur-Yvette and Guarulhos.

Largest cities, 2022–2025

  1. 1 Moscow Russia 792 works
  2. 2 Beijing China 734 works
  3. 3 Paris France 574 works
  4. 4 Tokyo Japan 490 works
  5. 5 Shanghai China 441 works
  6. 6 New York United States 238 works
  7. 7 Nanjing China 229 works
  8. 8 Seoul South Korea 228 works
  9. 9 London United Kingdom 226 works
  10. 10 Chennai India 219 works

Where it is the local speciality

  1. Huairou22.9 works60×
  2. Bures-sur-YvetteFR · 23.3 works52×
  3. GuarulhosBR · 70.6 works21×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Geometry and Topology than the world average.

See Geometry and Topology on the map

Geometry and Topology research by country

The best places for Geometry and Topology research inside each country, with that country's researchers and world standing.

Where is the best place to study Geometry and Topology?

Among universities, judged by research, Prince Sultan University, Moscow Institute of Physics and Technology and University of Oradea 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.

0%20%40%mean 22.81%fractional works in this node (log) →share in the world top 10% →Prince Sultan University: 40, 27.4%Moscow Institute of Physics and Technology: 44, 23.3%University of Oradea: 48, 32.0%National Research University Higher School of Economics: 150, 9.6%Sidi Mohamed Ben Abdellah University: 68, 19.1%University of Al-Qadisiyah: 66, 11.1%University of Management and Technology: 38, 23.0%COMSATS University Islamabad: 52, 28.9%Government College University, Lahore: 30, 25.2%China Medical University: 34, 28.5%University of OradeaPrince Sultan Univer…Moscow Institute of …National Research Un…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1Prince Sultan University Saudi Arabia 74.927.4%10.8×40 +401.9%
2Moscow Institute of Physics and Technology Russia 63.423.3%10.0×44 +134.8%
3University of Oradea Romania 62.332.0%16.9×48 -13.4%
4National Research University Higher School of Economics Russia 60.09.6%10.9×150 +113.8%
5Sidi Mohamed Ben Abdellah University Morocco 59.719.1%7.4×68 +199.1%
6University of Al-Qadisiyah Iraq 59.411.1%12.8×66 +716.7%
7University of Management and Technology Pakistan 59.223.0%11.8×38 —
8COMSATS University Islamabad Pakistan 58.328.9%6.6×52 +33.4%
9Government College University, Lahore Pakistan 57.725.2%9.6×30 +51.6%
10China Medical University Taiwan 56.228.5%7.2×34 —

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 Geometry and Topology research growing?

Output in 2018–2022 was 4% higher than in 2013–2017, peaking in 2023. The fastest-growing topics are Fixed Point Theorems Analysis, Graph theory and applications and Geometry and complex manifolds.

19801990200020102020
grewheldshrank

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.

  1. Fixed Point Theorems Analysis+117%
  2. Graph theory and applications+56%
  3. Geometry and complex manifolds+51%
  4. Analytic and geometric function theory+50%
  5. Morphological variations and asymmetry+46%
  6. Algebraic Geometry and Number Theory+30%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Geometry and Topology include?

Algebraic structures and combinatorial models: 42k fractional worksMathematics and Applications: 35k fractional worksAlgebraic Geometry and N…29kAlgebraic Geometry and Number Theory: 29k fractional worksAdvanced Differential Eq…24kAdvanced Differential Equations and Dynamical Systems: 24k fractional worksGeometric and Algebraic Topology: 23k fractional worksAdvanced Topology and Set Theory: 20k fractional worksGraph theory and applica…18kGraph theory and applications: 18k fractional worksFixed Point Theorems Analysis: 18k fractional worksGeometry and complex manifolds: 17k fractional worksMorphological variations and asymmetry: 14k fractional worksAnalytic and geometric function theory: 13k fractional works

Area is fractional works in that topic. Every name below is a page of its own.