2021
DOI: 10.48550/arxiv.2108.04929
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Parabolic subgroups of two-dimensional Artin groups and systolic-by-function complexes

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Cited by 2 publications
(5 citation statements)
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“…1. if G Γ is of spherical type (see [4]), 2. if G Γ is of FC-type and P 1 is of spherical type (see [10] which generalizes [11] where the result was obtained when both P 1 and P 2 are of spherical type), 3. if G Γ is of large type, that is m({u, v}) ≥ 3 for all {u, v} ∈ E (see [5]), 4.…”
Section: Introductionmentioning
confidence: 86%
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“…1. if G Γ is of spherical type (see [4]), 2. if G Γ is of FC-type and P 1 is of spherical type (see [10] which generalizes [11] where the result was obtained when both P 1 and P 2 are of spherical type), 3. if G Γ is of large type, that is m({u, v}) ≥ 3 for all {u, v} ∈ E (see [5]), 4.…”
Section: Introductionmentioning
confidence: 86%
“…if G Γ is a (2,2)-free two-dimensional Artin group, i.e. Γ does not have two consecutive edges labeled by 2 and the geometric dimension of G Γ is two ( [3]), 6. if G Γ is Euclidean of type Ãn or Cn ( [8]).…”
Section: Introductionmentioning
confidence: 99%
“…Then we easily see that α ′ is exactly the element of A X represented by the word πX ( α) ∈ (Σ X ⊔ Σ −1 X ) * . Proof of Part (1). Let α, β ∈ (Σ ⊔ Σ −1 ) * be two words that represent the same element of A.…”
Section: Proofsmentioning
confidence: 99%
“…We see that, if α is the element of A represented by α, then α, regarded as an element of π 1 (Sal(Γ)) = A, is represented by the loop γ( α). Let γ( α) be the lift of γ( α) in Sal(Γ) starting at o (1). We set u 0 = 1 ∈ W and, for i ∈ {1, .…”
Section: Proofsmentioning
confidence: 99%
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