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arXiv · 2607.11360

Local-to-global fixed point properties for graphical C(4)-T(4) and C(6) small cancellation complexes

Karol Duda·Huaitao Gui
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Abstract

Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with prescribed subgraphs in their Cayley graphs. We prove that torsion subgroups of groups defined by possibly infinite C(4)-T(4) graphical small cancellation presentations are finite. We also prove the corresponding result for groups defined by C(6) graphical small cancellation presentations under the additional assumption that the presentation is torsion-essentially C(6)-free. Both results follow from a more general result on local-to-global fixed point properties for torsion groups acting by automorphisms on simply connected graphical small cancellation complexes.

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Karol Duda, Huaitao Gui. 2026-07-13. Local-to-global fixed point properties for graphical C(4)-T(4) and C(6) small cancellation complexes. https://arxiv.org/abs/2607.11360

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