Michael Boardman

John Michael Boardman (1938-2021) was a British-born mathematician, specialised in algebraic topology and differential topology. He received his Ph.D. from the University of Cambridge in 1964. His thesis advisor was C. T. C. Wall. He was formerly at the University of Cambridge, England; later a full professor at Johns Hopkins University in Baltimore, USA.

Selected writings

Boardman introduced the stable homotopy category in 1969. His notes on this subject were never formally published, but Rainer Vogt gave a course on this subject in Aarhus in 1969:

He coauthored with Vogt the famous book

This book introduced the notion of weak Kan complex that was later popularized by André Joyal under the name quasi-category as a natural basis for the higher category theory of (∞,1)-categories.

See also: Homotopy invariant algebraic structures: a conference in honor of J. Michael Boardman edited by Jean-Pierre Meyer, Jack Morava, and W. Stephen Wilson. AMS, 1999, CONM/239.

Introducing the Boardman homomorphism:

On stable cohomology operations, but mostly reviewing the background of stable homotopy theory, Whitehead-generalized cohomology theory, ring spectra, multiplicative cohomology theory, complex oriented cohomology and the examples of KU, MU, BP:

On unstable cohomology operations (hence: in non-abelian cohomology):


Some of the above material is taken from Joyal's CatLab – Michael Boardman.

and Rainer Vogt’s article (with self explanatory title):

category: people