arXiv subjects

Huaitao Gui

Publications and source records attributed to Huaitao Gui.

3 recordsLinked to original sources

arXiv2026

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

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.

math.GR↗

arXiv2026

Fit systolic groups, exactly

A systolic complex/bridged graph is fit when its (metric) intervals are "not too large". We prove that uniformly locally finite fit systolic complexes have Yu's Property A. In particular, groups acting properly on such complexes have Property A, (equivalently) they are exact, and (equivalently) they are boundary amenable. As applications we show that groups from a class containing all large-type Artin groups, as well as all finitely presented graphical $C(3)$--$T(6)$ small cancellation groups, and finitely presented classical $C(6)$ small cancellation groups are exact. We also provide further examples. Our proof relies on a combinatorial criterion for Property~A due to Špakula and Wright.

math.GR↗

arXiv2026

Graphical C(3)-T(6) implies CAT(0)

Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with interesting features. In the classical setting, C(3)-T(6) small cancellation complexes are known to admit locally CAT(0) metrics. In this paper, we construct locally CAT(0) metrics for graphical C(3)-T(6) complexes.

math.GR↗