After have disengaged, starting from 1961, the structural role of some
topologic varieties of surface in relation whit the unconscious, Lacan
interests of 1972 to 1980 to the theory of knots. He is of stays to note
that the knot could be given by an edge of surface, or again be obtained
by a cut operated on this surface. It is the discovery of the existence
of the ?borromean knot? who seems inaugurate this period. Lacan finds a
configuration who goes him there "like ring to the finger," in the measurement
where she avers to be the adequate prop to the knotage between the Real,
the Imaginary and the Symbolic. All along the thread of the Seminaries,
he studies the different aftermath of mistakes of knotage between these
three consistences, and he articules between them, on the basis of the
concepts of the psychoanalysis, the intersticial fields of the borromean
knot ?put on flat?. Progressively, he introduces the concept of "sinthôme,"
as a fourth circle who comes hold borromeanely the three orders disunited.
He works with some mathematicians to the problem of retournement of enlaced
or slotted tores, and interests to the logic traps operated on some borromean
knots into these tores. Lacan makes proof of a diligent work of researcher.
It is also the opportunity of fundamental reflection on the position of
knowledge, mathematics and science.
The trefoil like edge of moebian surface :
Two prime knots studied by Lacan :
