The Todd-Coxeter process, using graphs. (English) Zbl 0619.20014

Combinatorial group theory and topology, Sel. Pap. Conf., Alta/Utah 1984, Ann. Math. Stud. 111, 157-161 (1987).
[For the entire collection see Zbl 0611.00010.]
The paper gives a description of the Todd-Coxeter method for the enumeration of the cosets of a subgroup of a finitely presented group in terms of operations on graphs. The description is based on notions explained in a paper by J. Stallings [Invent. Math. 71, 551-565 (1983; Zbl 0521.20013)]. The description is probably more conceptual than the usual one for people used to work with graphs or fundamental groups, but does not seem to lead to an improvement of the method.
Reviewer: J.Neubüser


20F05 Generators, relations, and presentations of groups
05C38 Paths and cycles
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
57M99 General low-dimensional topology