  In quantum geometry, we consider a set of loops, a compact orientable surface
and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3
\equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient
isotopic equivalence relation on such triples, so that we can obtain
equivalence invariants. These invariants describe how these submanifolds are
causally related to or `linked' with each other, and they are closely
associated with the linking number between links in $\mathbb{R}^3$. Because we
distinguish the time-axis from spatial subspace in $\mathbb{R}^4$, we see that
these equivalence relations, will also imply causality.
