Isotropic Systems

In this paper we introduce a combinatorial and algebraic structure called isotropic system. Some isotropic systems are associated to pairs of dual binary matroids, the sum-decomposable systems, and the other ones are associated to 4-regular graphs, the graphic systems, but there are isotropic systems which are neither graphic nor binary. The introduction of the paper describes the applications of isotropic systems that we have found at present and which will be developed in subsequent papers