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We introduce a geometry of interaction model for Mazza's multiportinteraction combinators, a graph-theoretic formalism which is able tofaithfully capture concurrent computation as embodied by process algebras likethe $\pi$-calculus. The introduced model is based on token machines in whichnot one but multiple tokens are allowed to traverse the underlying net at thesame time. We prove soundness and adequacy of the introduced model. The formeris proved as a simulation result between the token machines one obtains alongany reduction sequence. The latter is obtained by a fine analysis ofconvergence, both in nets and in token machines.

The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)