  Cobordism categories are known to be compact closed. They can therefore be
used to define non-degenerate models of multiplicative linear logic by
combining the Int construction with double glueing. In this work we detail such
construction in the case of low-dimensional cobordisms, and exhibit a connexion
between those models and the model of Interaction graphs introduced by Seiller.
In particular, we exhibit how the so-called trefoil property is a consequence
of the associativity of composition of higher structures, providing a first
step toward establishing models as obtained from a double glueing construction.
We discuss possible extensions to higher-dimensional cobordisms categories
