Science Explorer Interactive view Map
Topic · Mathematical Physics

Homotopy and Cohomology in Algebraic Topology

Homotopy and Cohomology in Algebraic Topology is a research topic within Mathematical Physics. Science Explorer counts 28k research works in it since 1950. 16.7% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the deformation quantization of Poisson manifolds, involving topics such as Lie algebroids, homotopy theory, symplectic geometry, model categories, K-theory, operads, and higher algebraic structures. It explores the application of deformation quantization in various mathematical contexts and its implications for understanding geometric and algebraic structures.

  • Deformation Quantization
  • Poisson Manifolds
  • Lie Algebroids
  • Homotopy Theory
  • Symplectic Geometry
  • Model Categories
  • K-Theory
  • Operads
  • Higher Algebraic Structures
  • Stacks
Research works
28k
fractional, since 1950
In the world top 10%
4.6k
per year above
Top-10% rate
16.7%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
0%
the tick is no change

Which countries lead Homotopy and Cohomology in Algebraic Topology research?

By volume, the United States and China publish the most (700 and 291 works in 2022–2025).

By volume, 2022–2025

  1. 1 United States 700 works
  2. 2 China 291 works
  3. 3 France 255 works
  4. 4 Germany 246 works
  5. 5 Japan 218 works
  6. 6 United Kingdom 215 works
  7. 7 Brazil 127 works
  8. 8 Italy 126 works
  9. 9 Russia 125 works
  10. 10 India 120 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: 28.9%China: 12.0%France: 10.5%Germany: 10.2%6 others listed: 38.4%29%largest
United States700 · 28.9%China291 · 12.0%France255 · 10.5%Germany246 · 10.2%6 others listed931 · 38.4%

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

Which institutions lead Homotopy and Cohomology in Algebraic Topology research?

By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Homotopy and Cohomology in Algebraic Topology research, followed by Faculdades Guarulhos and University of Oxford.

By volume, 2022–2025

  1. 1 Centre National de la Recherche Scientifique France 36 works
  2. 2 Faculdades Guarulhos Brazil 32 works
  3. 3 University of Oxford United Kingdom 30 works
  4. 4 Guarulhos University Brazil 28 works
  5. 5 Max Planck Institute for Mathematics Germany 26 works
  6. 6 Kyoto University Japan 23 works
  7. 7 The Ohio State University United States 18 works
  8. 8 Universidad Nacional Autónoma de México Mexico 18 works
  9. 9 Utrecht University Netherlands 18 works
  10. 10 The University of Tokyo Japan 17 works

Who are the leading researchers in Homotopy and Cohomology in Algebraic Topology?

The most-cited researchers publishing on Homotopy and Cohomology in Algebraic Topology include Shing–Tung Yau and Cumrun Vafa.

  1. 1 Shing–Tung Yau 2.1k citations
  2. 2 Cumrun Vafa 2.1k citations

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

Where is Homotopy and Cohomology in Algebraic Topology research done?

The largest centres of Homotopy and Cohomology in Algebraic Topology research in 2022–2025 are Paris (France), Moscow (Russia), Tokyo (Japan) and Beijing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Guarulhos and Bonn.

Largest cities, 2022–2025

  1. 1 Paris France 80 works
  2. 2 Moscow Russia 77 works
  3. 3 Tokyo Japan 69 works
  4. 4 Beijing China 65 works
  5. 5 Guarulhos Brazil 60 works
  6. 6 Bonn Germany 40 works
  7. 7 New York United States 36 works
  8. 8 Prague Czechia 35 works
  9. 9 Madrid Spain 33 works
  10. 10 London United Kingdom 31 works

Where it is the local speciality

  1. GuarulhosBR · 60.3 works175×
  2. BonnDE · 40.5 works16×
← less than its size predicts1×more →

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

See Homotopy and Cohomology in Algebraic Topology on the map

Where is the best place to study Homotopy and Cohomology in Algebraic Topology?

Among universities, judged by research, University of Regensburg, Stockholm University and University of Oxford 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 15.71%fractional works in this node (log) →share in the world top 10% →University of Regensburg: 16, 11.7%Stockholm University: 10, 22.2%University of Oxford: 30, 14.2%National Research University Higher School of Economics: 15, 9.4%University of Bonn: 14, 14.0%ETH Zurich: 16, 19.1%Utrecht University: 18, 10.9%Guarulhos University: 28, 0.0%Princeton University: 11, 28.8%Charles University: 11, 26.8%Stockholm UniversityUniversity of OxfordUniversity of Regens…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
1University of Regensburg Germany 59.911.7%29.0×16 +201.5%
2Stockholm University Sweden 52.722.2%8.8×10 +98.9%
3University of Oxford United Kingdom 50.814.2%7.0×30 +5.6%
4National Research University Higher School of Economics Russia 50.49.4%10.9×15 +111.3%
5University of Bonn Germany 50.014.0%12.8×14 +17.3%
6ETH Zurich Switzerland 49.219.1%7.2×16 +19.9%
7Utrecht University Netherlands 49.110.9%10.0×18 -22.6%
8Guarulhos University Brazil 48.20.0%373.5×28 —
9Princeton University United States 47.528.8%7.5×11 +15.4%
10Charles University Czechia 46.826.8%7.4×11 +0.8%

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 Homotopy and Cohomology in Algebraic Topology research growing?

Output in 2018–2022 was 0% lower than in 2013–2017, peaking in 2023. The fastest-growing topics are Homotopy and Cohomology in Algebraic Topology.

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.