Almost identical imitations of (3,1)-dimensional manifold pairs (Q914202)

In this paper, for a good compact oriented (3,1)-manifold pair (M,L), the concept of an almost identical imitation \((M,L^*)\) of (M,L) is introduced. The main result of this paper is the existence of an infinite family of almost identical imitations \((M,L^*)\) of (M,L) whose exteriors are hyperbolic. This confirms a conjecture of Simon and Wolcott on the existence as an almost trivial spatial graph of a planar graph.