Edgar H. Brown

Edgar Henry Brown junior (born December 27, 1926 in Oak Park , Illinois ) is an American mathematician who studies algebraic topology and differential topology .

life and work

Brown graduated from the University of Wisconsin with a bachelor's degree in 1949, from Washington State University with a master's degree in 1951, and received his doctorate in 1954 from the Massachusetts Institute of Technology with George William Whitehead ( Finite computability of the homotopy groups of finite groups ). 1954/55 he was an instructor at Washington University in St. Louis , 1955 to 1957 instructor at the University of Chicago and 1957/58 at Brown University as a fellow of the Office of Naval Research . Since 1958 he has been at Brandeis University , where he was given a full professorship in mathematics in 1963 and headed the faculty from 1960 to 1962 and from 1978 to 1980.

In 1962/63 he was at the Institute for Advanced Study , in 1965/66 as a Guggenheim Fellow at the University of Oxford , 1973/74 at University College London and 1982/83 visiting professor in Oxford and Cambridge . In 1993 he was visiting professor at Yale , 1986/87 at Jesus College, University of Oxford and 1971 visiting professor at Princeton University .

In his dissertation he proved the finite predictability of higher homotopy groups (not the fundamental group) of finite, simply connected simplicial complexes (this was already known for homology groups and Serre had previously shown the finite producibility). He also introduced Postnikov complexes in the Soviet Union independently of Mikhail Michailowitsch Postnikow .

A representation set (Representability Theorem) in homotopy theory is named after him.

Partly with Franklin Peterson, he also achieved results on the conditions for the existence of immersions in differential topology. With Peterson he introduced Brown-Peterson cohomologies in 1966.

Brown is a Fellow of the American Academy of Arts and Sciences and the American Mathematical Society . He was the US delegate for mathematics in the People's Republic of China . Douglas C. Ravenel is one of his PhD students .

He has been married since 1954 and has two children.

Fonts

Finite computability of Postnikov complexes , Annals of Mathematics 65, 1957, 1 (derived from the dissertation)
Cohomology theories , Annals of Mathematics, Volume 75, 1962, pp. 467-488
with Franklin Paul Peterson Relations among characteristic classes , I., Topology, Volume 3, 1964, pp. 39-52
with F. Peterson On immersions of n-manifolds , Advances in Mathematics, 24, 1977, 74-77
with F. Peterson Algebraic bordism groups , Annals of Mathematics, 79, 1964, 616-622
Abstract Homotopy Theory , Transactions AMS, 119, 1965, 79-85
Representability of functors in abstract homotopy theory , Transactions AMS, 119, 1965, 215-217
with F. Peterson, D. Anderson Spin cobordism , Bulletin AMS, 72, 1966, 256-260
with F. Peterson A universal space for normal bundles of n-manifolds , Comm. Math. Helveticae, 54, 1979, 405-430
with F. Peterson A spectrum whose cohomology is the algebra of reduced pth powers ${\ displaystyle Z_ {p}}$ , Topology 5, 1966, 149-154
with S. Gitler A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra , Topology, Volume 12, 1973, pp. 283-295.

literature

George W. Whitehead The work of Edgar H. Brown in Topology , in G. Carlsson, H. Miller, R. Cohen, D. Ravenel (Eds.) Algebraic Topology , Springer Verlag, Lecture Notes in Mathematics 1370, 1989, pp. 10-14

Web links

Homepage

Individual evidence

^ Edgar H. Brown in the Mathematics Genealogy Project (English)
↑ The results of his dissertation were partly published in Bulletin AMS, Volume 61, 1955, 55 (announcement) and Finite computability of Postnikov complexes , Annals of Mathematics 65, 1957, 1
^ GW Whitehead The work of EH Brown in Topology
↑ Jean Lannes La conjecture des immersions, d'après RL Cohen , Edgar H. Brown, FP Peterson et al., Séminaire Bourbaki 594, 1981/82, numdam ( Memento of October 2, 2013 in the Internet Archive )

personal data
SURNAME	Brown, Edgar H.
ALTERNATIVE NAMES	Brown, Edgar Henry Junior (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	December 27, 1926
PLACE OF BIRTH	Oak Park , Illinois

[1] Edgar H. Brown in the Mathematics Genealogy Project (English)

[2] The results of his dissertation were partly published in Bulletin AMS, Volume 61, 1955, 55 (announcement) and Finite computability of Postnikov complexes , Annals of Mathematics 65, 1957, 1

[3] GW Whitehead The work of EH Brown in Topology

[4] Jean Lannes La conjecture des immersions, d'après RL Cohen , Edgar H. Brown, FP Peterson et al., Séminaire Bourbaki 594, 1981/82, numdam ( Memento of October 2, 2013 in the Internet Archive )