Non-finite presentability of nonuniform lattices in locally finite polyhedral complexes

Let XX be a locally finite polyhedral complex, let G=Aut(X)G=\operatorname{Aut}(X), and let Γ\Gamma be a nonuniform lattice in GG. Non-finite presentability conjecture. The group Γ\Gamma is not finitely presentable. The source proposes this as a broad expectation motivated by the non-finite presentability of certain lattices in algebraic groups in positive characteristic; its general validity is open.

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Primary source

Benson Farb, G. Christopher Hruska and Anne Thomas, “Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices”, arXiv:0803.2484 (2008).

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