Mathematical formalization and diagrammatic reasoning: the case study of the braid group between 1925 and 1950

Figures & data

Figure 1. (a) Artin’s drawing of a concatenation of two braids (Artin 1926, 48). (b) A forbidden braid (ibid.) (c) A drawing of the generator σ_i (ibid., 49)

Figure 2. Inducing the relation σ_i σ_i+1 σ_i = σ_i+1 σ_i σ_i+1 (Artin 1926, 51)

Figure 3. A drawing of the braid a⁴, which commutes with all other braids in the braid group of four strings (Artin 1926, 54)

Figure 4. Artin’s drawing for illustrating a cut of a closed braid (Artin 1926, 55)

Figure 5. A drawing of Burau, depicting the points A and B and the two classes of strings, denoted by α and β (Burau 1932, 118)

Figure 6. Fröhlich’s depiction of finding the fundamental curves of K (Fröhlich 1936, 227)

Artin, Emil, ‘Theorie der Zöpfe’, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 4 (1926), 47–72. doi: 10.1007/BF02950718

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Burau, Werner, ‘Über Zopfinvarianten’, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 9 (1932), 117–124. doi: 10.1007/BF02940634

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Fröhlich, W., ‘Über ein spezielles Transformationsproblem bei einer besonderen Klasse von Zöpfen’, Monatshefte für Mathematik und Physik, 44 (1936), 225–237. doi: 10.1007/BF01699317

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