Hiroshi Toda

Q: What Schools Are Affiliated With Hiroshi Toda

Hiroshi Toda is affiliated with the following schools: University of Tokyo, Kyoto University

Hiroshi Toda's AcademicInfluence.com Rankings

Hiroshi Toda

Mathematics

#1560

World Rank

#2538

Historical Rank

Algebraic Geometry

#181

World Rank

#189

Historical Rank

Measure Theory

#2903

World Rank

#3451

Historical Rank

mathematics Degrees

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Mathematics

Hiroshi Toda's Degrees

PhD Mathematics University of Tokyo

Why Is Hiroshi Toda Influential?

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According to Wikipedia, Hiroshi Toda 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 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 . Here he uses as important tools the Toda bracket and the Toda fibration, among others, to compute the first 20 nontrivial homotopy groups for each sphere.

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Hiroshi Toda's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Composition Methods in Homotopy Groups of Spheres (1962) (337)
Topology of Lie Groups, I and II (1991) (146)
On spectra realizing exterior parts of the steenrod algebra (1971) (130)
Multiplicative structures in mod q cohomology theories. I (1965) (125)
Generalized Whitehead products and homotopy groups of spheres (1952) (78)
Localization of CW-complexes and its applications (1971) (68)
Cohomology operations and the homotopy of compact lie groups—I (1970) (67)
On the double suspension E^2 (1956) (64)
$p$-primary components of homotopy groups IV. Compositions and toric constructions (1959) (59)
A topological proof of theorems of Bott and Borel-Hirzeburch for homotopy groups of unitary groups (1959) (57)
Mod p Decomposition of Compact Lie Groups (1977) (57)
Order of the Identity Class of a Suspension Space (1963) (57)
On the cohomology ring of some homogeneous spaces. (1975) (55)
The $(n+20)$-th homotopy groups of $n$-spheres (1963) (54)
On Jacobi identity for Whitehead products (1954) (47)
An important relation in homotopy groups of spheres (1967) (40)
Extended p-th Powers of Complexes and Applications to Homotopy Theory (1968) (39)
Onp-equivalences andp-universal spaces (1971) (36)
Algebra of stable homotopy of $Z_p$-spaces and applications (1971) (34)
On iterated suspensions III. (1965) (32)
Hopf Algebra Structure of mod 2 Cohomology of Simple Lie Groups (1976) (32)
Cohomology mod 3 of the classifying space $BF_4$ of the exceptional group $F_4$ (1973) (32)
A note on stunted lens space (1966) (31)
NOTE ON COHOMOLOGY RING OF CERTAIN SPACES (1963) (30)
The integral cohomology rings of $F_4/T$ and $E_6/T$ (1974) (29)
On the cohomology of irreducible symmetric spaces of exceptional type (1977) (27)
$p$-primary components of homotopy groups III. Stable groups of the sphere (1958) (22)
On p-equivalence in the sense of Serre (1971) (20)
$p$-primary components of homotopy groups II. mod $p$ Hopf invariant (1958) (18)
On the Structure of $H^*(BSF; Z_p)$. (1967) (15)
On exact sequences in Steenrod algebra mod. 2 (1958) (13)
Note on the generator of $\pi_7(SO(n))$ (1957) (13)
On the classification of $H$-spaces of rank 2 (1973) (13)
On homotopy groups of $S^3$-bundles over spheres (1962) (12)
Complex of the standard paths and n-ad homotopy groups (1955) (11)
A note on compact semi-simple Lie groups (1976) (11)
Squaring operations on truncated polynomial algebras (1969) (11)
The symplectic Lazard ring (1982) (11)
$p$-primary components of homotopy groups I. Exact sequences in Steenrod algebra (1958) (10)
On the homotopy groups of spheres (1952) (8)
Non-triviality of an element in the stable homotopy groups of spheres (1975) (7)
Topology of Standard Path Spaces and Homotopy Theory. I (1953) (6)
Vector fields on spheres (1961) (6)
Segal-Becker theorem for $KR$-theory (1982) (5)
A representation and the quasi p-regularity of the compact Lie group (1975) (4)
Reduced join and Whitehead product (1957) (4)
Non-existence of mappings of $S^{31}$ into $S^{16}$ with Hopf invariant 1 (1957) (3)
Mod p decomposition of lie groups (1971) (2)
3-primary $\beta $-family in stable homotopy (1975) (0)
On Mod 3 Characteristic Classes for $F_4$-Bundles (Geometry of Manifolds) (1972) (0)

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What Schools Are Affiliated With Hiroshi Toda?

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Hiroshi Toda's Academic­Influence.com Rankings

Hiroshi Toda's Degrees

Why Is Hiroshi Toda Influential?

Hiroshi Toda's Published Works

Published Works

Other Resources About Hiroshi Toda

What Schools Are Affiliated With Hiroshi Toda?

Hiroshi Toda's AcademicInfluence.com Rankings