Geodesic
An embedding for π2 of a subcomplex of a finite contractible two-complex
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 365-371

Voir la notice de l'article provenant de la source Cambridge University Press

A longstanding open question in low dimensional topology was raised by J. H. C. Whitehead in 1941 [9]: “Is any subcomplex of an aspherical, two-dimensional complex itself aspherical?” The asphericity of classical knot complements [7] provides evidence that the answer to Whitehead's question might be “yes”. Indeed, each classical knot complement has the homotopy type of a two-complex which can be embedded in a finite contractible two-complex. This property is shared by a large class of four-manifolds; these are the ribbon disc complements, whose asphericity has been conjectured, and even claimed, but never proven. (See [4] for a discussion.) It is reasonable and convenient to formulate the following. 
Bogley, William A. An embedding for π2 of a subcomplex of a finite contractible two-complex. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 365-371. doi: 10.1017/S0017089500008430
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[1] 1.Bourbaki, N., Lie groups and Lie algebras, Chapters 1–3 (Springer-Verlag, 1989). Google Scholar

[2] 2.Cockroft, W. H., On two-dimensional aspherical complexes, Proc. London Math. Soc. (3) 4 (1954), 375–384. Google Scholar | DOI

[3] 3.Gutierrez, M. and Ratcliffe, J., On the second homotopy group, Quart. J. Math. Oxford Ser. (2) 32 (1981), 45–55. Google Scholar | DOI

[4] 4.Howie, J., On the asphericity of ribbon disc complements, Trans. Amer. Math. Soc. 289 (1985), 281–302. Google Scholar | DOI

[5] 5.Lyndon, R. C., Cohomology theory of groups with a single defining relation, Ann. of Math. (2) 52 (1950), 650–665. Google Scholar | DOI

[6] 6.Magnus, W., Über Beziehungen zwischen höheren Kommutatoren, J. Reine Angew. Math. 177 (1937), 105–115. Google Scholar | DOI

[7] 7.Papakyriakopoulos, C. D., On Dehn's lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. Google Scholar | DOI

[8] 8.Stallings, J., Homology and central series of groups, J. Algebra 2 (1965), 170–181. Google Scholar | DOI

[8] 8.Whitehead, J. H. C., On adding relations to homotopy groups, Ann. of Math. (2) 42 (1941), 409–428. Google Scholar | DOI

[10] 10.Witt, E., Treue Darstellung Liescher Ringe, J. Reine Angew. Math. 177 (1937), 152–160. Google Scholar | DOI

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