On Decompositions in Homotopy Theory
Brayton Gray
55P35, 5P30, 55P45
Dept. of Mathematics, Statistics and Computer Science (M/C 249)
University of Illinois at Chicago
851 South Morgan Street
Chicago, IL 60607-7045
brayton@uic.edu
We first describe Krull-Schmidt theorems decomposing $H$ spaces and
simply connected co-$H$ spaces into atomic factors in the category of
pointed nilpotent $p$-complete spaces of finite type. We use this to
construct a 1-1 correspondence between homotopy types of atomic $H$
spaces and homotopy types of atomic co-$H$ spaces, and construct a split
fibration which connects them and illuminates the decomposition. Various
properties of these constructions are analyzed.