Homology of proof-nets

This work defines homology groups for proof-structures in multiplicative linear logic (see Gir1], Gir2], Dan]). We will show that these groups characterize proof-nets among arbitrary proof-structures, thus obtaining a new correctness criterion and of course a new polynomial algorithm for testing correctness. This homology also bears information on sequentialization. An unexpected geometrical interpretation of the linear connectives is given in the last section. This paper exclusively focuses onabstract proof-structures, i.e. paired-graphs. The relation with actual proofs is investigated in Gir1], Gir2], Dan], Ret] and Tro].