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Freiheitssätze for one-relator quotients of surface groups and of limit groups. (English) Zbl 1183.20041

Authors’ summary: Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published corresponding statements for one-relator quotients of orientable surface groups. Two of the proofs are new even in that restricted context.

MSC:

20F65 Geometric group theory
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F05 Generators, relations, and presentations of groups
20E08 Groups acting on trees
20E18 Limits, profinite groups
57M07 Topological methods in group theory
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