Geodesic
The K(π,1) conjecture and acylindrical hyperbolicity for relatively extra-large Artin groups
Goldman, Katherine M1
1 Department of Mathematics, Ohio State University, Columbus, OH, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1487-1504

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Let AΓ be an Artin group with defining graph Γ. We introduce the notion of AΓ being extra-large relative to a family of arbitrary parabolic subgroups. This generalizes a related notion of AΓ being extra-large relative to two parabolic subgroups, one of which is always large type. Under this new condition, we show that AΓ satisfies the K(π,1) conjecture whenever each of the distinguished subgroups do. In addition, we show that AΓ is acylindrically hyperbolic under only mild conditions.

DOI : 10.2140/agt.2024.24.1487
Keywords: Artin group, Deligne complex, CAT(0), geometric group theory, complex of groups, metric simplicial complex

Goldman, Katherine M 1

1 Department of Mathematics, Ohio State University, Columbus, OH, United States 
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Goldman, Katherine M. The K(π,1) conjecture and acylindrical hyperbolicity for relatively extra-large Artin groups. Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1487-1504. doi: 10.2140/agt.2024.24.1487

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