ABSTRACT
This chapter deals with a very important historical issue which can be related to a structural dimension: the study on graphs was carried out by Euler, one of the most prolific mathematicians in history; that study on graphs by Euler is the basis of topology. This means that topology not only enters psychoanalysis via the graphs, but it enters mathematics by the same route. In J. Lacan's teaching, the series built with models, schemata, graphs, topologic surfaces and knots takes an exclusive place and significance. The argument is that optical model responds to Lacan's theory of the topography of the unconscious. There is no other psychoanalyst who has given such importance, given so much time and consideration to this problem of representations in psychoanalysis. The chapter argues that the graph of desire was not topological, that topology was the Mobius strip, the torus, the cross-cap and Klein's bottle—the four topological surfaces.
