Strictly systolic angled complexes and hyperbolicity of one-relator groups

Short, highly imprimitive words yield hyperbolic one-relator groups

“…Since α is a W I conjugate of an element of W II , α ∈ W II . Thus there is an element of W II that takes w 1 to α (w 1 ) ∼ σ 1 (u 1 2 ), which is in the same PCI ± class as u 2 , so w 2 is the SLPCI ± minimal representative of α (w 1 ).…”

“…multiples of 1 2 ((L − 7) 2 + 11(L − 7) + 30), with a unique largest component of size L−7 2 ((L − 7) 2 + 11(L − 7) + 30) represented by C L−8 BCACaBAA. Myasnikov and Shpilrain [24] proved that components of the Whitehead level-L graph in rank r = 2 have size bounded by a polynomial of degree 2r − 2 in L, see also [19,5], and conjectured that this should be true in higher ranks (see the conjecture and discussion following [24,Corollary 1.2]).…”

“…If Ivanov-Schupp does not apply, then (3) check if w satisfies one of the small cancellation conditions C(7), C(5)−T (4), C(4)−T (5), or C(3)−T (7), in which case G is hyperbolic via results of Gersten and Short [9]. Otherwise, (4) check if w satisfies the C (1/4)−T hyperbolicity condition of Blufstein and Minian [1]. If not, (5) check hyperbolicity of G with GAP.…”

“…These results are achieved computationally, by a combination of efficient enumeration of representatives and brute force 1 . Details are in Section 4.…”