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F. R. Cohen - On stunted projective spaces
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 6-skeleton of the Lie
group G2. 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 X2 gives a different
proof of a theorem of Jie Wu concerning a splitting of the homotopy
groups for
.



Next: Gustavo Granja - On HPn Up: 2) Homotopy Theory / Théorie Previous: Dan Christensen - Phantom