Geodesic
The Whitehead conjecture~-- an overview
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 440-449.

Voir la notice de l'article provenant de la source Math-Net.Ru

These notes are an elaboration of a talk held November 3, 2006 at the “Metzler Fest” in honour of Wolfgang Metzler's 65-th birthday at the university of Frankfurt. The aim is to give an overview of results concerning Whitehead's asphericity conjecture. 
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S. Rosebrock. The Whitehead conjecture~-- an overview. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 440-449. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a33/

[1] J. F. Adams, “A new proof of a theorem of W. H. Cockcroft”, Journal of the London Math. Soc., 30 (1955), 482–488 | DOI | MR | Zbl

[2] Bestvina M. and Brady N., “Morse theory and finiteness properties of groups”, Invent. Math., 129 (1997), 445–470 | DOI | MR | Zbl

[3] W. A. Bogley, “J. H. C. Whitehead's asphericity question”, Two-Dimensional Homotopy and Combinatorial Group Theory, LMS Lecture Notes, 197, eds. C. Hog-Angeloni, A. Sieradski and W. Metzler, Cambridge University Press, 1993, 309–334 | MR | Zbl

[4] Cockcroft W. H., “On two-dimensional aspherical complexes”, Proc. London Math. Soc. (3), 4 (1954), 375–384 | DOI | MR | Zbl

[5] Steve Gersten, Reducible diagrams and equations over groups. Essays in group theory, Math. Sci. Res. Ins. Publ., 8, Springer Verlag, 1987 | MR

[6] Jens Harlander and Stephan Rosebrock, “Generalized knot complements and some aspherical ribbon disc complements”, Knot theory and its Ramifications, 12:7 (2003), 947–962 | DOI | MR | Zbl

[7] James Howie, “Aspherical and acyclic 2-complexes”, J. London Math. Soc., 20:3 (1979), 549–558 | DOI | MR | Zbl

[8] James Howie, “Some remarks on a problem of J. H. C. Whitehead”, Topology, 22 (1983) | MR

[9] James Howie, “On the asphericity of ribbon disk complements”, Trans A.M.S., 289:1 (1985) | MR | Zbl

[10] Guenther Huck and Stephan Rosebrock, “Ein verallgemeinerter Gewichtstest mit Anwendungen auf Baumpräsentationen”, Mathematische Zeitschrift, 211 (1992), 351–367 | DOI | MR | Zbl

[11] Guenther Huck and Stephan Rosebrock, “Aspherical Labelled Oriented Trees and Knots”, Proc. Edinb. Math. Soc. (2), 44:2 (2001), 285–294 | DOI | MR | Zbl

[12] Guenther Huck and Stephan Rosebrock, “Spherical Diagrams and Labelled Oriented Trees”, Proceedings of the Edinburgh Math. Soc., 50 (2007) | Zbl

[13] E. Luft, “On 2-dimensional aspherical complexes and a problem of J. H. C. Whitehead”, Math. Proc. Cambridge Phil. Soc., 119 (1996), 493–495 | DOI | MR | Zbl

[14] Stephan Rosebrock, “A reduced spherical diagram into a ribbon–disk complement and related examples”, Lecture Notes in Mathematics, 1440, ed. P. Latiolais, Springer Verlag, 1990, 175–185 | MR

[15] Stephan Rosebrock, “Some aspherical labelled oriented graphs”, Low-Dimensional Topology and Combinatorial Group Theory, Proceedings of the International Conference, ed. S. Matveev, Kiev, 2000

[16] Stephan Rosebrock, On the complexity of labelled oriented trees, Preprint, 2007 | MR

[17] J. H. C. Whitehead, “On adding relations to homotopy groups”, Ann. of Math., 42:2 (1941) | DOI | MR