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On the Andrews-Curtis-conjecture and related problems. (English) Zbl 0579.57003
Combinatorial methods in topology and algebraic geometry, Proc. Conf. Hon. A. M. Stone, Rochester/N.Y. 1982, Contemp. Math. 44, 35-50 (1985).
[For the entire collection see Zbl 0564.00013.]
This survey article deals with the connection of group presentations and the simple homotopy type of complexes. Discussed are the Q-equivalences of group presentations (an equivalence under restricted changes of presentations) and applications mainly to the theory of 2-complexes and 3-manifolds.
Reviewer: H.Zieschang

57M20 Two-dimensional complexes (manifolds) (MSC2010)
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57M05 Fundamental group, presentations, free differential calculus
57N10 Topology of general \(3\)-manifolds (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
20F05 Generators, relations, and presentations of groups