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Stable summands of U(n)

Published online by Cambridge University Press:  14 November 2011

M. C. Crabb ,
J. R. Hubbuck  and
J. A. W. McCall
M. C. Crabb
Affiliation:
Department of Mathematical Sciences, University of Aberdeen AB24 3QY, Scotland, U.K.
J. R. Hubbuck
Affiliation:
Department of Mathematical Sciences, University of Aberdeen AB24 3QY, Scotland, U.K.
J. A. W. McCall
Affiliation:
School of Computer and Mathematical Sciences, The Robert Gordon University, Aberdeen AB25 1HG, Scotland, U.K.
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Synopsis

The 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 963 - 973
Copyright
Copyright © Royal Society of Edinburgh 1997

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