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Constructions and 3-deformations of 2-polyhedra and group presentations. (English) Zbl 0832.57001
In dieser Arbeit werden einige Äquivalenzen zwischen geometrischen und algebraischen Versionen des Andrews-Curtis-Problems bewiesen. Die Sachverhalte sind zumeist bekannt [C. Hog-Angeloni und der Referent, Lond. Math. Soc. Lect. Note Ser. 197, 365-380, 381-407 (1993; Zbl 0814.57002); ibid. 1-50, 381-407 (1993; Zbl 0811.57001); C. Hog- Angeloni and A. J. Sieradski, ibid. 251-280, 381-407 (1993; Zbl 0811.57006); A. J. Sieradski, ibid. 51-96, 381-407 (1993; Zbl 0811.57002)]. Der Akzent der Beweise liegt in der Benutzung von 2- Komplexen allgemeiner Lage. Noch nicht publiziert wurde m.W. das Ergebnis, daß für Präsentationen, bei denen jede Erzeugende genau 3 Vorkommnisse in den Relatoren hat, im Fall von höchstens 3 Erzeugenden die Andrews-Curtis-Vermutung richtig ist.
MSC:
57M20 Two-dimensional complexes (manifolds) (MSC2010)
57M05 Fundamental group, presentations, free differential calculus
20F65 Geometric group theory
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