Subject: for the list
From: "W. Stephen Wilson"
Date: Mon, 21 Aug 2006 11:05:01 -0400
>From Japan:
Dear Steve,
I visited Kudo's house with Masayoshi Kamata, Mitsuyoshi Kato,
Yasumasa Hirashima, Nobuyuki Oda and Kazuyuki Fujii and met his
wife. The following is our short obituary for Tatsuji Kudo.
This obituary is based on Minoru Tomita's article "Tatsuji Kudo
--- professional career and works" (Mem. Fac. Sci. Kyusyu Univ,
Ser. A. 38 (1984), 1-4) and Fank Adams' review on the paper of
Dyer-Lashof "Homology of iterated loop spaces" (Amer. J. Math.
84 (1962), 35-88).
Best Regards, Norio Iwase
--
Tatsuji Kudo died on 7th of August at the age of 86. His wife
told us that he had cancers of stomach and lung for several
years. Until very recently, he visited hospital four or five
days a week for the treatment. But he could not survive the
hottest days of this summer.
Kudo was born on 18th of November 1919 in Nagano prefecture,
Japan and graduated Osaka University. Under the supervision
of Atuo Komatu, Kudo published his first paper on problem of
stability of complexes raised by H. Hopf and E. Pannwitz as
"Contribution to the problem of stability" (Osaka Math. J. 1
(1949), 62-72).
Kudo published two papers on his idea to calculate homology
groups of fibre-bundles as "Homological properties of fibre
bundles" (J. Inst. Polytechn. Osaka City U. Ser. A 1 (1950),
101-114) and "Homological structures of fibre bundles" (J.
Inst. Polytechn. Osaka City Univ. Ser. A 2 (1952), 101-140)).
His idea is calculating the subquotients of relative homology
groups associated with the filtration of total space which is
induced from the skeletal filtration of the base space, which
can now be understood as the Leray spectral sequence and was
established independently.
The next important work of Kudo is a theorem known as Kudo's
Transgression Theorem which is an important tool to calculate
mod p cohomology of Eilenberg-Mac Lane spaces (Mem. Fac. Sci.
Kyushu Univ. Ser. A 9 (1956), 79-81). With Shoro Araki, Kudo
investigated homotopy property of iterated loop spaces and
published two papers introducing an operad which measures
higher structures of homotopy commutativity, together with
homology operations which are known as Kudo-Araki operations
(Proc. Japan Acad. 32 (1956), 333-335, Mem. Fac. Sci. Kyusyu
Univ, Ser. A. 10 (1956), 85-120).
Later by W. Browder, Kudo-Araki operations are defined more
generally on homotopy commutative Hopf spaces and applied to
study torsion in such spaces. On the other hand, following
the pattern established by Kudo and Araki, E. Dyer and R. K.
Lashof introduced a mod p homology operation for p odd, which
plays now an important role in studying infinite loop spaces.
From his early careers of mathematics, Kudo was interested in
category theory and axiomatic homotopy theory. One goal of
the study is on additive relations in abelian category (Rep.
Fac. Sci. Engrg. Saga Univ. Math. 11 (1983), 9-25). Kudo also
showed how to construct his spectral sequence using additive
relations in a course lecture for graduate students.
Kudo encouraged many young mathematicians as a professor of
Kyushu University. Those who know him well might remember
that he enjoyed alcohol and cigarettes quite a lot as well as
mathematics in his life. But his wife told us that he did
not have alcohol much and had no cigarettes in these days.
We are sure he is enjoying alcohol and cigarettes a lot as
well as mathematics in the heaven.
Nobuhiro Ishikawa Masayoshi Kamata
Mitsuyoshi Kato Yasumasa Hirashima
Nobuyuki Oda Kazuyuki Fujii
Norio Iwase
--