A non-acylindrically hyperbolic Morse local-to-global group

Abstract: Hyperbolic spaces satisfy two defining properties: every geodesic is Morse, and every local quasi-geodesic (on a sufficiently large local scale) is a global quasi-geodesic. In non-hyperbolic spaces, some geodesics may be Morse and others not, and local quasi- geodesics may or may not be global quasi-geodesics. Intuitively, the Morse geodesics pick out the “hyperbolic-like” directions in the space. Morse local-to-global (MLTG) spaces generalize hyperbolic spaces by requiring that the local-to-global property for hyperbolic spaces holds for all Morse elements. MLTG groups (groups whose Cayley graph is a MLTG space) include hyperbolic groups, Zn, many classes of Artin groups, including right-angled, mapping class groups, and groups hyperbolic relative to MLTG groups. All known examples that contain a Morse element are acylindrically hyperbolic; in light of which Russell, Spriano, and Tran asked whether this was always the case. In this talk, I’ll explain why the answer to this question is no by describing the construction of a non-acylindrically hyperbolic MLTG group with a Morse element. Along the way, I’ll describe how to generalize several techniques from small cancellation groups to general finitely generated groups.

This is joint work with Stefanie Zbinden.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

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Geometry and topology online

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The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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