ON THE HOMOTOPY TYPE OF INFINITE STUNTED PROJECTIVE SPACES 
By: F. R. Cohen and R. Levi 

To appear in the 1998 Barcelona Conference Proceedings 

AMS Classification: 55R35 

Address: 
Fred Cohen, Department of Mathematics, University of Rochester, 
Rochester, NY 14627, U.S.A. 
Ran Levi, Department of Mathematical Sciences, University of Aberdeen, 
Aberdeen, AB24 3UE, Scotland 


Let $X_n$ denote the infinite stunted projective space ${\Bbb 
R}P^\infty/{\Bbb R}P^{n-1}$. In this note we study the homotopy type 
of this family of spaces. In particular we show that for $n=2 $ and 4, 
the space $X_n$ splits after looping once and for $n=3$ after looping 
four times and passing to connected covers. In each case the factors 
are loop spaces on naturally occuring finite complexes. These result 
generalise to higher values of $n$, but in those cases without a 
splitting result. The splittings enable us to carry out a calculation 
of low dimensional homotopy and loop space homology for these spaces, 
which complements a computer calculation of Sergeraert and Smirnov. A 
number of interesting related facts and questions is also discussed.