Fig. 6

A decomposition of a bistructure (LHS) and the evolution of its loop nerve (RHS). LHS: exposed vertices are labelled red. RHS: the loops 1, 2, 3, 5 and 6 form a sphere. Removing one loop from this sphere is tantamount to deleting one vertex of the loop nerve. The white vertices in the loop nerve represent the boundary of the substructure. The sphere corresponding to the crossing component is resolved by removing the S-arc