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Geometric aspects of two-dimensional complexes. (English) Zbl 0811.57001
Hog-Angeloni, Cynthia (ed.) et al., Two-dimensional homotopy and combinatorial group theory. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 197, 1-50, 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 first chapter contains a detailed introduction to the geometric aspects of two-dimensional complexes along with many examples. The main headings are 1. Complexes of low dimensions and group presentations; 2. Simple-homotopy and low dimensions; 3. P.L. embeddings of 2-complexes into manifolds; 4. Three conjectures and further problems. Beginning with the definition of CW-complexes, the authors take the reader on a tour of two-dimensional complexes that ends with a discussion of the generalized Andrews-Curtis conjecture, the Zeeman collapsing conjecture, and the Whitehead asphericity conjecture.
For the entire collection see [Zbl 0788.00031].

MSC:
57M20 Two-dimensional complexes (manifolds) (MSC2010)
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57Q35 Embeddings and immersions in PL-topology
57M05 Fundamental group, presentations, free differential calculus
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