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On 2-dimensional aspherical complexes and a problem of J. H. C. Whitehead

Published online by Cambridge University Press:  24 October 2008

E. Luft
E. Luft
Affiliation:
Mathematics Department, University of British Columbia, 121–1984 Mathematics Road, Vancouver, B.C., Canada, V6T 1Z2
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Extract

In [W] J. H. C. Whitehead posed the following question: ‘Is every subcomplex K of a 2-dimensional aspherical complex L itself aspherical ?’

This problem is usually referred to as the ‘Whitehead Conjecture’ though it was only stated in the form of a question. For convenience we treat it also as a conjecture.

The Whitehead Conjecture has been proved in special cases: if the subcomplex K has only one 2-cell, and also in the case where π1(K) is either finite, abelian, of free [C] For more partial results see, for example, the introduction of [H1].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 493 - 495
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[C]Cockcroft, W. H.. On two-dimensional aspherical complexes. Proc. London Math. Soc. (3) 4 (1954), 375–384.CrossRefGoogle Scholar
[H1]Howie, J.. Aspherical and acyclic 2-complexes. J. London Math. Soc. (2) 20 (1979), 549–558.CrossRefGoogle Scholar
[H2]Howie, J.. Some remarks on a problem of J. H. C. Whithead. Topology 22 (1983), 475–485.CrossRefGoogle Scholar
[W]Whithead, J. H. C.. On adding relations to homotopv groups. Ann. Math. 42 (1941), 409–428.CrossRefGoogle Scholar