Hiroshi Toda (戸田 宏, Toda Hiroshi, born 1928) is a Japanese mathematician, who specializes in stable and unstable homotopy theory. He started publishing in 1952. Many of his early papers are concerned with the study of Whitehead products and their behaviour under suspension and more generally with the (unstable) homotopy groups of spheres. In a 1957 paper he showed the first non-existence result for the Hopf invariant 1 problem. This period of his work culminated in his book Composition methods in homotopy groups of spheres (1962). Here he uses as important tools the Toda bracket (which he calls the toric construction) and the Toda fibration, among others, to compute the first 20 nontrivial homotopy groups for each sphere.
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| - Hiroshi Toda (en)
- هيروشي تودا (ar)
- Hiroshi Toda (de)
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| - هيروشي تودا (باليابانية: 戸田宏) هو رياضياتي ياباني، ولد في 1928 في اليابان. (ar)
- Hiroshi Toda (jap. 戸田 宏, Toda Hiroshi; * 1928 in Japan) ist ein japanischer Mathematiker, der sich mit Topologie beschäftigt. Toda wurde 1956 an der Universität Osaka promoviert. Er war danach Professor in Kyōto. 1957 wurde er mit dem Asahi-Preis ausgezeichnet. 1959 bis 1961 war er am Institute for Advanced Study in Princeton. Toda ist für seine Arbeiten zur Berechnung der Homotopiegruppen von Sphären bekannt. Die dort verwendete Technik des „Toda-Bracket“ ist nach ihm benannt. Er sollte nicht mit dem Physiker Morikazu Toda (1917–2010), dem Entdecker des Toda-Gitters, verwechselt werden. (de)
- Hiroshi Toda (戸田 宏, Toda Hiroshi, born 1928) is a Japanese mathematician, who specializes in stable and unstable homotopy theory. He started publishing in 1952. Many of his early papers are concerned with the study of Whitehead products and their behaviour under suspension and more generally with the (unstable) homotopy groups of spheres. In a 1957 paper he showed the first non-existence result for the Hopf invariant 1 problem. This period of his work culminated in his book Composition methods in homotopy groups of spheres (1962). Here he uses as important tools the Toda bracket (which he calls the toric construction) and the Toda fibration, among others, to compute the first 20 nontrivial homotopy groups for each sphere. (en)
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| - هيروشي تودا (باليابانية: 戸田宏) هو رياضياتي ياباني، ولد في 1928 في اليابان. (ar)
- Hiroshi Toda (jap. 戸田 宏, Toda Hiroshi; * 1928 in Japan) ist ein japanischer Mathematiker, der sich mit Topologie beschäftigt. Toda wurde 1956 an der Universität Osaka promoviert. Er war danach Professor in Kyōto. 1957 wurde er mit dem Asahi-Preis ausgezeichnet. 1959 bis 1961 war er am Institute for Advanced Study in Princeton. Toda ist für seine Arbeiten zur Berechnung der Homotopiegruppen von Sphären bekannt. Die dort verwendete Technik des „Toda-Bracket“ ist nach ihm benannt. Er sollte nicht mit dem Physiker Morikazu Toda (1917–2010), dem Entdecker des Toda-Gitters, verwechselt werden. (de)
- Hiroshi Toda (戸田 宏, Toda Hiroshi, born 1928) is a Japanese mathematician, who specializes in stable and unstable homotopy theory. He started publishing in 1952. Many of his early papers are concerned with the study of Whitehead products and their behaviour under suspension and more generally with the (unstable) homotopy groups of spheres. In a 1957 paper he showed the first non-existence result for the Hopf invariant 1 problem. This period of his work culminated in his book Composition methods in homotopy groups of spheres (1962). Here he uses as important tools the Toda bracket (which he calls the toric construction) and the Toda fibration, among others, to compute the first 20 nontrivial homotopy groups for each sphere. Among his most important contributions to stable homotopy theory is his work on the existence and non-existence of so-called Toda–Smith complexes. These are finite complexes which can be characterized as having a particularly simple ordinary homology (as modules over the Steenrod algebra) or, alternatively, by having a particularly simple BP-homology. They can be used to construct the Greek letter infinite families in the stable homotopy groups of spheres. In his paper On spectra realizing exterior parts of the Steenrod algebra (1971), Toda deduced several existence and non-existence results on these complexes. The existence parts are still unsurpassed. Toda did also important work on the algebraic topology of (exceptional) Lie groups. (en)
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