zbMATH — the first resource for mathematics

J. H. C. Whitehead’s asphericity question. (English) Zbl 0811.57008
Hog-Angeloni, Cynthia (ed.) et al., Two-dimensional homotopy and combinatorial group theory. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 197, 309-334, 381-407 (1993).
The present knowledge of the relation of two-dimensional homotopy to decision problems in combinatorial group theory is the subject of this important work that has both the elements of a textbook and a research monograph. This tenth chapter is concerned with Whitehead’s asphericity question: “Is any subcomplex of an aspherical, 2-dimensional complex itself aspherical?” [J. H. C. Whitehead, Ann. Math., II. Ser. 42, 409-428 (1941; Zbl 0027.26404)]. The author provides a summary of the published results and an overview of the methods that have been used in the study of the problem.
For the entire collection see [Zbl 0788.00031].

57M20 Two-dimensional complexes (manifolds) (MSC2010)
57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)