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 also did important work on the algebraic topology of (exceptional) Lie groups.
HiroshiToda (戸田 宏, TodaHiroshi, born 1928) is a Japanese mathematician, who specializes in stable and unstable homotopy theory. He started publishing...
Stage Directed by Shin'ichi Masaki Produced by Kayo Fukuda Written by HiroshiToda Nobuaki Kishima Music by Ryuichi Katsumata Studio Pastel Licensed by...
series Directed by Toyoo Ashida Produced by Yoshio Takami Written by HiroshiToda Music by Nozomi Aoki Studio Toei Animation Licensed by NA: Discotek Media...
(Akira Kogane, Takashi Shirogane, Isamu Kurogane, Tsuyoshi Seidou and Hiroshi Suzuichi) return to Earth from their latest space exploration, only to...
mathematics, the Toda bracket is an operation on homotopy classes of maps, in particular on homotopy groups of spheres, named after HiroshiToda, who defined...
Stephen Smale Edwin Spanier Norman Steenrod Dennis Sullivan René Thom HiroshiToda Leopold Vietoris Hassler Whitney J. H. C. Whitehead Gordon Thomas Whyburn...
elements. HiroshiToda used the composition product and Toda brackets to label many of the elements of homotopy groups. There are also higher Toda brackets...
Nicolas Avruj The Silver Crow Pheasant Award for the Best Director – HiroshiToda for Summer, Kyoto The Silver Crow Pheasant Award for the Best Debut Director...
animation Directed by Takashi Watanabe Produced by Kayo Fukuda Written by HiroshiToda Nobuhiko Horie Music by Yasuharu Takanashi -yaiba- (performance) Studio...
Morio Maejima Written by Tokio Tsuchiya, Izō Hashimoto, Noboru Sugimura, HiroshiToda, Ichirō Yamanaka Studio Toei Original network Fuji TV Original run November...
animated by Anime R [ja], directed Toru Yoshida [ja], with scripts by HiroshiToda [ja], was released on May 21, 1997. In North America, the OVA was licensed...
International Film Festival of Kerala Winner – Asian Competition Summer, Kyoto (HiroshiToda, Japan) Winner – Malayalam Competition Oraalppokkam (Sanal Kumar Sasidharan...
the Japanese school of homotopy theory, following in the tradition of HiroshiToda. Nishida received his Ph.D. from Kyoto University in 1973, after spending...
ayaushi Panikku Kōsutā" (Japanese: ミコちゃんあやうし パニックコースター) Takaya Mizutani HiroshiToda June 25, 1984 (1984-06-25) The Kyunkyuns, and Chikkun and Takkun go to...
by: Reiko Mutō (1st series), Keiko Toda (2nd series) Portrayed by: Yuri Shirahane The English teacher at Hiroshi's school. Both Umesaburo and Mr. Minami...
to attend a Buddhist discussion meeting. It was there that he met Josei Toda, the second president of Japan's Soka Gakkai Buddhist organization. Ikeda...
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