On the homotopy groups of 2-cell complexes
Brayton Gray
55Q20
Department 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
In 1978, Cohen, Moore, and Neisendorfer gave a decomposition of the loops
on a mod p^r Moore space when p>2. This decomposition involved an atomic
factor T^(2n+1) which was encompassed in a fibration sequence with other
terms whose homotopy was better understood. This paper considers the case
when the mod p^r Moore space is replaced by the mapping cone P of an
element in an even stem. Exactly the same results are obtained when the
attaching map is divisible by p, or the dimension of P is even. The
first obstruction to such a result is displayed in general, and the
example of beta_1 is presented.