Finite rigid sets in curve complexes of nonorientable surfaces

Ilbıra, Sabahattin; Korkmaz, Mustafa

doi:10.1007/s10711-019-00478-6

Cited by 6 publications

(2 citation statements)

References 16 publications

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“…This type of result was originally suggested by Lars Louder. Such has been shown for the curve complex (Aramayona-Leininger [3], Ilbira-Korkmaz [13], Irmak [16] and [15]), the arc complex (the author [38]), and the pants graph (Maungchang [31], Hernández-Hernández-Leininger-Maungchang [12], Maungchang [30]). We prove such a result for the flip graph in this paper.…”

Section: Introductionmentioning

confidence: 94%

Finite Rigid Sets in Flip Graphs

Shinkle¹

2020

Preprint

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We show that for most pairs of surfaces, there exists a finite subgraph of the flip graph of the first surface so that any injective homomorphism of this finite subgraph into the flip graph of the second surface can be extended uniquely to an injective homomorphism between the two flip graphs. Combined with a result of Aramayona-Koberda-Parlier in [2], this implies that any such injective homomorphism of this finite set is induced by an embedding of the surfaces.

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Section: Introductionmentioning

confidence: 94%

Finite Rigid Sets in Flip Graphs

Shinkle¹

2020

Preprint

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“…In subsequent work, they also constructed an exhaustion of the curve complex C(S) = ∪ n X n by a nested sequence of finite rigid subcomplexes X n [3]. Subsequently, a plethora of surface complexes have been shown to have (exhaustions by) finite rigid sets [9,10,12,13,19,20,23,24].…”

Section: Introductionmentioning

confidence: 99%

Finite rigid sets in sphere complexes

Bering¹,

Leininger²

2022

Preprint

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A subcomplex X ≤ C of a simplicial complex is rigid if every locally injective, simplicial map X → C is the restriction of an automorphism of C. Aramayona and the second author proved that the curve complex of an orientable surface can be exhausted by finite rigid sets. The Hatcher sphere complex is an analog of the curve complex for isotopy classes of essential spheres in a connect sum of n copies of S 1 × S 2 . We show that there is an exhaustion of the sphere complex by finite rigid sets for all n ≥ 3 and that when n = 2 the sphere complex does not have finite rigid sets.

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Finite rigid sets in sphere complexes

Bering,

Leininger

2024

Topology and its Applications

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Finite rigid sets in curve complexes of nonorientable surfaces

Cited by 6 publications

References 16 publications

Finite Rigid Sets in Flip Graphs

Finite Rigid Sets in Flip Graphs

Finite rigid sets in sphere complexes

Finite rigid sets in sphere complexes

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