On the work of Fred Cohen. Part I --- the first 25 years.
I will trace first half of Fred's long career.
Fred's earliest work was on conguration spaces which he used, among other applications, to compute the homology of $k$-fold iterated loop suspensions. His work with co-authors Larry Taylor and his thesis advisor, Peter May, on this subject stable wedge decompositions which became one of the themes of Fred's work throughout his career.
In the late 1970s he entered the field of Classical Unstable Homotopy Theory, as he joined with Joe Neisendorfer and John Moore to produce a string of spectacular results obtained by constructing product decompositions up-to-homotopy. I will discuss the general idea of the proof of their homotopy-exponent theorem for spheres along with the general method of constructing product decompositions they pioneered.
In the 1990s Fred directed a lot of his attention towards attempting to prove a conjecture of Michael Barratt on the largest possible order of an element in the homotopy of a co-$H$-space in which the the identity map
has finite order. Although he never succeeded in this main goal, it resulted in ideas on combinatorial group theory which were later applied by Fred and others.
Fred's wrote a huge volume of papers on a large variety of topics with a multitude of co-authors. At any time, aside whatever his main focus may have been, he produced a large number of important papers on other subjects. Calculations were an integral part of his work and created the intuition behind many of his theorems.
While he continued to develop and add new topics, he never forgot his roots and one continues to find papers on configuration spaces and braids throughout his career as well as in the theses and later work of his graduate students.
The lecture will conclude with a few of the ideas of which Fred was particularly fond.