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Topic · Geometry and Topology

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. 9.9% 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%
2.3k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+28%
the tick is no change
Largest producer
United States
31% of the 10 largest, 2022-now
Geometric and Algebraic Topology

Which countries lead Geometric and Algebraic Topology research?

By volume, the United States and China publish the most (809 and 326 works in 2022-now).

By volume, 2022-now

  1. 1 United States 809 works
  2. 2 China 326 works
  3. 3 France 258 works
  4. 4 Japan 252 works
  5. 5 Germany 215 works
  6. 6 United Kingdom 215 works
  7. 7 Russia 189 works
  8. 8 India 144 works
  9. 9 Italy 123 works
  10. 10 Brazil 112 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: 30.6%China: 12.3%France: 9.8%Japan: 9.5%6 others listed: 37.8%31%largest
United States809 · 30.6%China326 · 12.3%France258 · 9.8%Japan252 · 9.5%6 others listed998 · 37.8%

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

Which institutions lead Geometric and Algebraic Topology research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Geometric and Algebraic Topology research, followed by Russian Academy of Sciences and University of Oxford.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 125 works
  2. 2 Russian Academy of SciencesRussia 52 works
  3. 3 University of OxfordUnited Kingdom 31 works
  4. 4 National Research University Higher School of EconomicsRussia 30 works
  5. 5 Kyoto UniversityJapan 27 works
  6. 6 Max Planck SocietyGermany 25 works
  7. 7 The Ohio State UniversityUnited States 25 works
  8. 8 ETH ZurichSwitzerland 24 works
  9. 9 Lomonosov Moscow State UniversityRussia 22 works
  10. 10 City University of New YorkUnited States 20 works

Who are the leading researchers in Geometric and Algebraic Topology?

The most-cited researchers publishing on Geometric and Algebraic Topology include Edward H. Witten, B. S. Acharya and Minghui Liu.

  1. 1 Edward H. Witten United States 174k citations
  2. 2 B. S. Acharya France 164k citations
  3. 3 Minghui Liu France 137k citations
  4. 4 Andrew Y. Ng United States 131k citations
  5. 5 A. Haas France 130k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Geometric and Algebraic Topology?

The most cited paper in Geometric and Algebraic Topology is "Hirshfeld surface analysis" (Mark A. Spackman, Dylan Jayatilaka, 2008), with 8,008 citations. Next come "Quantum field theory and the Jones polynomial" (4,977) and "Introduction: Motivation" (2,273).

Most cited papers
#PaperReleasedCitations
1 Hirshfeld surface analysis Mark A. Spackman, Dylan Jayatilaka · CrystEngComm 21 Nov 2008 8,008
2 Quantum field theory and the Jones polynomial Edward H. Witten · Communications in Mathematical Physics Sep 1989 4,977
3 Introduction: Motivation Chris Wendl · Cambridge University Press eBooks Book chapter 6 Mar 2020 2,273
4 Short Group Signatures Dan Boneh, Xavier Boyen, Hovav Shacham · Lecture notes in computer science Conference paper 2004 2,109
5 Pseudo holomorphic curves in symplectic manifolds Mikhail Leonidovich Gromov · Inventiones mathematicae Jun 1985 2,092
All 99 most cited papers, with filters and sorting

Where is Geometric and Algebraic Topology research done?

The largest centres of Geometric and Algebraic Topology research in 2022-now 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-now

  1. 1 MoscowRussia 110 works
  2. 2 TokyoJapan 83 works
  3. 3 ParisFrance 76 works
  4. 4 BeijingChina 75 works
  5. 5 New YorkUnited States 43 works
  6. 6 ShanghaiChina 39 works
  7. 7 KyotoJapan 33 works
  8. 8 OxfordUnited Kingdom 31 works
  9. 9 SeoulSouth Korea 31 works
  10. 10 ZurichSwitzerland 29 works

Where it is the local speciality

  1. GuarulhosBR · 22.0 works63×
  2. PrincetonUS · 26.3 works12×
  3. BonnDE · 28.2 works11×
← less than its size predicts1×more →

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

See Geometric and Algebraic Topology on the map

Where is the best place to study Geometric and Algebraic Topology?

Among universities, judged by research, ETH Zurich, University of Oxford 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.

0%20%40%mean 20.14%fractional works in this field (log) →share of work in the world top 10% →Princeton UniversityUniversity of Cambri…ETH ZurichUniversity of Oxford
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1ETH ZurichSwitzerland 82.015.5%10.8×24 +59.7%
2University of OxfordUnited Kingdom 78.312.4%7.0×31 +87.9%
3Princeton UniversityUnited States 76.624.8%11.6×16 +20.6%
4University of CambridgeUnited Kingdom 73.517.1%5.0×19 +25.6%
5Massachusetts Institute of TechnologyUnited States 71.525.2%7.3×16 -11.5%
6National Research University Higher School of EconomicsRussia 67.912.1%23.7×30 +54.8%
7Yale UniversityUnited States 66.131.7%3.5×12 +165.5%
8University of California, BerkeleyUnited States 62.528.6%3.7×11 +6.6%
9University of WarwickUnited Kingdom 62.111.9%11.1×16 +140.1%
10University of California, DavisUnited States 61.822.1%5.4×14 +39.1%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Geometric and Algebraic Topology, country by country

Is Geometric and Algebraic Topology research growing?

Output in 2022-2025 was 28% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Geometric and Algebraic Topology.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Geometric and Algebraic Topology as a percentage of every work published that year, 0.015% in 2024.

still counting0.020%0.040%Geometric and Algebraic Topology0.015% in 202519801990200020102020

Fractional works of Geometric and Algebraic Topology over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Geometric and Algebraic Topology9.8% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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