Negative immersions for one-relator groups

Louder, Larsen; Wilton, Henry

doi:10.1215/00127094-2021-0024

Cited by 14 publications

(12 citation statements)

References 33 publications

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“…There are now a lot of examples, besides the ones here, which are consistent with this conjecture. As a partial converse, groups with a strong form of non-positive Euler characteristic are expected to be coherent [Wis03,LW18]. Similarly, we have Theorem 3.5.…”

Section: Introductionmentioning

confidence: 67%

Incoherence of free-by-free and surface-by-free groups

Kropholler,

Vidussi,

Walsh

2020

Preprint

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Section: Introductionmentioning

confidence: 67%

Incoherence of free-by-free and surface-by-free groups

Kropholler,

Vidussi,

Walsh

2020

Preprint

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“…With the definitions of irreducibility in hand, we can now define non-positive and negative immersions. These definitions are inspired by Wise [Wis03,Wis20], and similar definitions have played a role in several recent papers about onerelator groups, such as [HW16,LW17,LWar]. They are also naturally related to the work of Martínez-Pedroza and Wise on sectional curvature for 2-complexes [Wis04,Wis08,MPW13].…”

Section: Curvature Conditionsmentioning

confidence: 99%

“…Stallings famously popularised the folding operation for graphs [Sta83]. In [LWar,LW20], we made use of a folding operation on morphisms of 2-complexes that produces immersions. Here we will make use of a very natural folding operation on morphisms of 2-complexes that produces branched immersions.…”

Section: Various Kinds Of Mapsmentioning

confidence: 99%

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Uniform negative immersions and the coherence of one-relator groups

Louder,

Wilton

2021

Preprint

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Previously, the authors proved that the presentation complex of a onerelator group G satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G is free. Here, we prove that one-relator groups with negative immersions are coherent, answering a question of Baumslag in this case. Other strong constraints on the finitely generated subgroups also follow such as, for example, the co-Hopf property. The main new theorem strengthens negative immersions to uniform negative immersions, using a rationality theorem proved with linear-programming techniques.

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“…Negative immersions. Louder and Wilton in [LW18] introduced the concept of a negative immersion for two-dimensional CW-complexes (for a comparison with the stronger notation of negative immersions in the sense of Wise [Wis20], see [LW21, Section 3.4]). In the same paper, they give a group theoretic characterisation of negative immersions for presentation complexes of one-relator groups.…”

Section: Connectionsmentioning

confidence: 99%