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

  • E. Luft (a1)

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].

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[C]Cockcroft W. H.. On two-dimensional aspherical complexes. Proc. London Math. Soc. (3) 4 (1954), 375384.
[H1]Howie J.. Aspherical and acyclic 2-complexes. J. London Math. Soc. (2) 20 (1979), 549558.
[H2]Howie J.. Some remarks on a problem of J. H. C. Whithead. Topology 22 (1983), 475485.
[W]Whithead J. H. C.. On adding relations to homotopv groups. Ann. Math. 42 (1941), 409428.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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