We show the existence of several new infinite families polynomially-growing automorphisms free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such thick, and thus not relatively hyperbolic. These first comprising infinitely many examples for each rank nonabelian group; they contrast strongly with Gersten’s example a thick group which cannot be subgroup group.

Abstract In a seminal paper, Stallings introduced folding of morphisms graphs. One consequence is the representation finitely-generated subgroups finite-rank free group as immersions finite Stallings’s methods allow one to construct this algorithmically, giving effective, algorithmic answers and proofs classical questions about groups. Recently Dani–Levcovitz used Stallings-like study right-ang...

Abstract We give another proof of Toyoda’s theorem that describes 5-point subspaces in CAT(0) length spaces.

We prove that the 7-strand braid group is CAT(0) by elaborating on argument of Haettel, Kielak, and Schwer.