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Calculating generators of $$\pi_ 2$$. (English) Zbl 0811.57005
Hog-Angeloni, Cynthia (ed.) et al., Two-dimensional homotopy and combinatorial group theory. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 197, 157-188, 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 monomorph. This fifth chapter uses the theory of pictures in a discussion of combinatorial geometric techniques that determine explicit generators for the second homotopy module of a 2-complex in terms of its cell structure. The last section contains a summary description without proofs of various calculations and applications that have been obtained in the study of $$\pi_ 2$$.
For the entire collection see [Zbl 0788.00031].

##### MSC:
 57M20 Two-dimensional complexes (manifolds) (MSC2010) 57N65 Algebraic topology of manifolds 55Q05 Homotopy groups, general; sets of homotopy classes