9 papers
Finite complete rewriting systems for graphs of free groups with applications to free-by-cyclic, one-relator, and three-manifold groups
Robert D. Gray, Marco Linton
We prove that any finite graph of finitely generated free groups admits a finite complete rewriting system after possibly taking a free product with a free group of rank two. As a…
Coherent RFRS groups
Sam P. Fisher, Marco Linton, Pablo Sánchez-Peralta
We prove that a finitely generated virtually RFRS group of cohomological dimension at most is coherent if and only if its second -Betti number vanishes if and only if it…
The finitely generated intersection property in fundamental groups of graphs of groups
Jordi Delgado, Marco Linton, Jone Lopez de Gamiz Zearra +2
A group is said to satisfy the finitely generated intersection property (f.g.i.p.) if the intersection of any two finitely generated subgroups of is again finitely generate…
Group pairs, coherence and Farrell--Jones Conjecture for
Andrei Jaikin-Zapirain, Marco Linton, Pablo Sánchez-Peralta
A group pair consists of a group together with a -set . Such a pair encodes properties of relative to the stabilisers of points in . In this paper, we sho…
Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups
Marco Linton
We refine Feighn--Handel's results on subgroups of mapping tori of free groups to the special case of free-by-cyclic groups. We use these refinements to show that any finitely gene…
Pullbacks and intersections in categories of graphs of groups
Jordi Delgado, Marco Linton, Jone Lopez de Gamiz Zearra +2
We develop a categorical framework for studying graphs of groups and their morphisms, with emphasis on pullbacks. More precisely, building on classical work by Serre and Bass, we g…
The theory of one-relator groups: history and recent progress
Marco Linton, Carl-Fredrik Nyberg-Brodda
The theory of one-relator groups is now almost a century old. The authors therefore feel that a comprehensive survey of this fascinating subject is in order, and this document is a…
Lifting relations in right orderable groups
Marco Linton
In this article we study the following problem: given a chain complex of free -modules, when is isomorphic to the cellular chain complex of some simply con…
Residually rationally solvable one-relator groups
Marco Linton
We show that the intersection of the rational derived series of a one-relator group is rationally perfect and is normally generated by a single element. As a corollary, we characte…