How to reach me:
by email: brayton@math.uic.edu
office phone: 312-996-4828 leave a message
on the answering machine if I am not available.
fax : 312-996-1491 be sure my bname is on the
document.
Education:
Thesis: Operations and a problem of Heller, supervised by
Michael Barratt. This thesis dealt with maps whose restriction to each
skeleton is inessential. They were called Heller maps in the thesis, but
in a later paper I renamed them phantom maps.
Algebraic Topology, and specifically, homotopy theory. The homotopy groups of spheres and related spaces has been both the laboratory and the playground for understanding the homotopy category. The global structure of the homotopy category is visible in the data when carefully analyzed. In particular, the periodic structure is seen before it's vast implications come to light. Most interesting is the gradual emerging understanding of the similarities and differences between the stable category and the unstable category.
See Math Sci for reviews of some of my papers. MathSci
My 1975 book, homotopy theory:An introduction to algebraic topology, published in the Academic Press Series of Monographs and Texts (# 64), is a unique development in that it develops homotopy theory geometrically, and derives homology and cohomology as a corollary. This is opposite to the traditional view, and leads to characteristic axioms on a fairly large category of spaces.
Teaching - Spring 2002:
Personal Interests: about
me