Contractibility of Δ_{S,S'} via a convex geodesic bicombing metric for non-exceptional types

Develop and verify that for any Artin group A_S and any almost spherical subset S'⊂S whose type is not in {\widetilde F_4, \widetilde E_6, \widetilde E_7, \widetilde E_8, [3,5,3], [5,3,3,3]}, the metric prescribed in Definition 2.6 on the relative Artin complex Δ_{S,S'} yields a metric space with convex geodesic bicombing (in the sense of Descombes–Lang), and consequently prove that Δ_{S,S'} is contractible.

Background

To avoid high-dimensional link complexities, the paper proposes a non-Euclidean metric assignment (Definition 2.6) on Δ_{S,S'} depending on a dominating Euclidean-type Coxeter system. The aim is to obtain a convex geodesic bicombing rather than CAT(0), yielding contractibility.

This conjecture targets all almost spherical types except the listed exceptional cases, and, if proven, would establish contractibility of the relevant cores needed for the global K(pi,1) strategy.