Above the Horizon there is no Sky

This paper takes one of Lacan’s “o objects” – the look – as its starting point. Lacan developed his thinking on the implications of perspective geometry for painting in 1966 in his seminar on The Object of Psychoanalysis where he showed its importance in Velasquez’s Las Meninas. Georgin and Porge develop the linkages between projective geometry and topology in order to show the gap which exists between the look and the gaze – the look being on the side of the subject and the gaze being on the side of the object, hence opening up a gap which is one of the avatars of the cross-cap. It is to the illumination of the link between the imaginary aspect of one of these o-objects – the look – and one ofits topological presentations, that this article contributes, by focusing on a precise point of this link.…