A Remark on the Geometrical Meaning of Multiplicative Connectives

We propose a simple model of Multiplicative Linear Logic based on the category of bordisms. The latter category has recently become important in current mathematics due to developments in topological field theory. The model has an extremely intuitive geometric description. Dual multiplicative connectives ⊗ and ℘ correspond roughly speaking to disjoint unions and connected sums of bordisms; as a consequence the Mix rule ⊗ ⊦ ℘ is not supported. This is a remarkable difference from the most of known models. Following the ideas of topological quantum field theory we also discover deep relationships of this new model to the coherent phase spaces model of the author, which is based on the context of symplectic geometry. We think that these relationships may serve in the future as a basis for modeling full Linear Logic as well as for putting LL in the context of modern mathematical and physical ideas