
F. R. COHEN, Department of Mathematics, University of Rochester, Rochester, New York 14627, USA 
On stunted projective spaces 
F. Sergeraert and V. Smirnov have recently studied the homology of the loop spaces for . It is the purpose of this note to record the homotopy type of these spaces after looping (sometimes more than once). The following is joint work with R. Levi.
Theorem. (1)
is homotopy equivalent to
.
(2)
is the homotopy theoretic fibre of a map
where Z denotes the 6skeleton of the Lie
group G_{2}. Thus
is homotopy equivalent to
.
(3)
is homotopy equivalent to
.
(4)
is the homotopy theoretic fibre of a map from a
finite complex to the Lie group
Spin(n).
Further information concerning the map is given. For example, the theorem above for X_{2} gives a different proof of a theorem of Jie Wu concerning a splitting of the homotopy groups for .