Stable summands of U(n)

1997 ◽  
Vol 127 (5) ◽  
pp. 963-973 ◽  
Author(s):  
M. C. Crabb ◽  
J. R. Hubbuck ◽  
J. A. W. McCall
Keyword(s):  
Homotopy Type ◽  
Unitary Group ◽  
Stable Homotopy ◽  
Finite Complex ◽  
Special Unitary Group ◽  
Prime 2

SynopsisThe special unitary group SU(n) has the stable homotopy type of a wedge of n − 1 finite complexes. The ‘first’ of these complexes is ΣℂPn–1, which is well known to be indecomposable at the prime 2 whether n is finite or infinite. We show that the ‘second’ finite complex is again indecomposable at the prime 2 when n is finite, but splits into a wedge of two pieces when n is infinite.

On the Stable Homotopy Type of Thom Complexes

1973 ◽  
Vol 25 (6) ◽  
pp. 1285-1294 ◽  
Author(s):  
R. P. Held ◽  
D. Sjerve
Keyword(s):  
Vector Bundle ◽  
Homotopy Type ◽  
Stable Homotopy ◽  
Homotopy Equivalence ◽  
Real Vector ◽  
Fiber Homotopy

Let α be a real vector bundle over a finite CW complex X and let T(α;X) be its associated Thorn complex. We propose to study the S-type (stable homotopy type) of Thorn complexes in the framework of the Atiyah-Adams J-Theory. Therefore we focus our attention on the group JR(X) which is defined to be the group of orthogonal sphere bundles over X modulo stable fiber homotopy equivalence.

The non-existence of odd primary Arf invariant elements in stable homotopy

1978 ◽  
Vol 83 (3) ◽  
pp. 429-443 ◽  
Author(s):  
Douglas C. Ravenel
Keyword(s):  
Spectral Sequence ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Arf Invariant ◽  
Prime 2

In this paper we will show that certain elements of order p (p an odd prime) on the 2-line of the Adams-Novikov spectral sequence support non-trivial differentials and therefore do not detect elements in the stable homotopy groups of spheres. These elements are analogous to the so-called Arf invariant elements of order 2, hence the title. However, it is evident that the methods presented here do not extend to the prime 2.

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