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We prove the Tits Alternative for groups acting on $2$-dimensional"recurrent" complexes with uniformly bounded cell stabilisers. This class ofcomplexes includes, among others: $2$-dimensional Euclidean buildings,$2$-dimensional systolic complexes, $B(6)$-small cancellation complexes, andstandard Cayley complexes for Artin groups of extra-large type. In the appendixwritten jointly with Jon McCammond we extend the result to a class of$2$-dimensional Artin groups containing all large-type Artin groups.

Tits Alternative for groups acting properly on $2$-dimensional recurrent complexes (with an appendix written jointly with Jon McCammond)