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- Hiroshi_Toda abstract "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.".
- Hiroshi_Toda birthDate "1928".
- Hiroshi_Toda birthYear "1928".
- Hiroshi_Toda wikiPageExternalLink fulltext.pdf.
- Hiroshi_Toda wikiPageExternalLink fulltext.pdf.
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- Hiroshi_Toda wikiPageWikiLink Brown–Peterson_cohomology.
- Hiroshi_Toda wikiPageWikiLink CW_complex.
- Hiroshi_Toda wikiPageWikiLink Category:1928_births.
- Hiroshi_Toda wikiPageWikiLink Category:20th-century_Japanese_mathematicians.
- Hiroshi_Toda wikiPageWikiLink Category:21st-century_Japanese_mathematicians.
- Hiroshi_Toda wikiPageWikiLink Category:Living_people.
- Hiroshi_Toda wikiPageWikiLink EHP_spectral_sequence.
- Hiroshi_Toda wikiPageWikiLink Homotopy.
- Hiroshi_Toda wikiPageWikiLink Homotopy_groups_of_spheres.
- Hiroshi_Toda wikiPageWikiLink Hopf_invariant.
- Hiroshi_Toda wikiPageWikiLink Japan.
- Hiroshi_Toda wikiPageWikiLink Lie_group.
- Hiroshi_Toda wikiPageWikiLink Mathematician.
- Hiroshi_Toda wikiPageWikiLink Singular_homology.
- Hiroshi_Toda wikiPageWikiLink Stable_homotopy_theory.
- Hiroshi_Toda wikiPageWikiLink Steenrod_algebra.
- Hiroshi_Toda wikiPageWikiLink Suspension_(topology).
- Hiroshi_Toda wikiPageWikiLink Toda_bracket.
- Hiroshi_Toda wikiPageWikiLink Toda–Smith_complex.
- Hiroshi_Toda wikiPageWikiLink Whitehead_product.
- Hiroshi_Toda wikiPageWikiLinkText "Hiroshi Toda".
- Hiroshi_Toda wikiPageWikiLinkText "Toda, Hiroshi".
- Hiroshi_Toda dateOfBirth "1928".
- Hiroshi_Toda name "Toda, Hiroshi".
- Hiroshi_Toda shortDescription "Japanese mathematician".
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- Hiroshi_Toda description "Japanese mathematician".
- Hiroshi_Toda description "Japanese mathematician".
- Hiroshi_Toda subject Category:1928_births.
- Hiroshi_Toda subject Category:20th-century_Japanese_mathematicians.
- Hiroshi_Toda subject Category:21st-century_Japanese_mathematicians.
- Hiroshi_Toda subject Category:Living_people.
- Hiroshi_Toda hypernym Mathematician.
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- Hiroshi_Toda type Scientist.
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- Hiroshi_Toda type Q215627.
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- Hiroshi_Toda comment "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.".
- Hiroshi_Toda label "Hiroshi Toda".
- Hiroshi_Toda sameAs Q1620287.
- Hiroshi_Toda sameAs Hiroshi_Toda.
- Hiroshi_Toda sameAs m.03cft_d.
- Hiroshi_Toda sameAs Q1620287.
- Hiroshi_Toda wasDerivedFrom Hiroshi_Toda?oldid=673510415.
- Hiroshi_Toda givenName "Hiroshi".
- Hiroshi_Toda isPrimaryTopicOf Hiroshi_Toda.
- Hiroshi_Toda name "Hiroshi Toda".
- Hiroshi_Toda name "Toda, Hiroshi".
- Hiroshi_Toda surname "Toda".