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Small cancellation theory over Burnside groups

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NPCW01 - Non-positive curvature in action

Co-author: Rémi Coulon (Université de Rennes 1)
I will discuss how combinatorics and geometry work together to provide a new and easy-to-apply tool for constructing infinite bounded torsion groups with prescribed properties. The main tools are acylindrical actions of (classical or graphical) small cancellation groups on hyperbolic spaces and the theory of periodic quotients of groups admitting such actions. As applications, we obtain Gromov monsters with bounded torsion, we show the unsolvability of numerous decision problems in categories of bounded torsion groups, and we obtain a Rips construction for bounded torsion groups. This is joint work with Rémi Coulon.

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