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[[Lacan]] used the [[concept ]] or [[image]] of the [[borromean knot|knot]] quite frequently. References to [[knot]]s can be found in [[Lacan]]'s [[Works of Jacques Lacan|work]] as early as the 1950s,<ref> {{E}} p. 281</ref> but it is not until the ealy 1970s that [[Lacan]] begins to examine [[knot]]s from the point of view of their [[topology|topological properties]]. In the mid-1970s he tried to theorize the interrelation of the [[Symbolic]], the [[Imaginary]] and the [[Real]] in [[terms ]] of the [[topology]] of [[borromean knot|knots]].

The study of "[[knot|knot theory]]" marks an important [[development ]] in [[Lacan]]'s [[topology]]; from the study of surfaces (the [[moebius strip]], the [[torus]], etc.) [[Lacan]] moves to a much more [[complex ]] area of the [[topology]] of [[knot]]s. [[Topology]] is increasingly seen as a radically [[metaphor|non-metaphorical]] way of exploring the [[symbolic order]] and its interactions with the [[imaginary]] and the [[real]]; rather than simply representing [[structure]], [[topology]] is that [[structure]].

In this late period of his [[work]], one kind of [[knot]] comes to interest [[Lacan]] more than any [[other]]: the [[Borromean knot]]. The [[Borromean knot]] -- shown to the [[right ]] -- so called because the [[List of Figures|figure]] is found on the coat of arms of the Borromeo [[family]], is a group of [[three ]] rings which are linked in such a way that if any one of [[them ]] is severed, all three become separated.<ref>{{S20}} p. 112</ref>

Strictly [[speaking]], it would be more appropriate to refer to this [[figure ]] as a [[chain]] rather than a [[knot]], since it involves the interconnection of several different threads, whereas a [[knot]] is formed by a single thread. Although a minimum of three threads or rings are required to [[form ]] a [[Borromean knot|Borromean chain]], there is no maximum [[number]]; the [[chain]] may be extended indefinitely by adding further rings, while still preserving its [[Borromean knot|Borromean]] quality (i.e. if any of the rings is cut, the [[whole ]] chain falls apart).

[[Lacan]] first takes up the [[Borromean knot]] in the [[seminar]] of 1972-3, but his most detailed [[discussion ]] of the [[knot]] comes in the [[seminar]] of 1974-5. It is in this [[seminar]] that [[Lacan]] uses the [[Borromean knot]] as, among other things, a way of illustrating the interdependence of the [[order|three order]]s of the [[real]], the [[symbolic]] and the [[imaginary]], as a way of exploring what it is that these [[order|three order]]s have in common. Each ring represents one of the [[order|three order]]s, and thus certain elements can be located at intersections of these rings. (In his view these [[orders ]] are tied together in the form of a "Borromean knot". The "Borromean knot" is a linkage of three "string rings" in such a way that no two rings intersect. The structure of the knot is such that the cutting of any one ring will liberate all of the [[others]]. [[Lacan]] used the [[theory ]] of knots to stress the relations which [[bind ]] or link the [[Imaginary]], [[Symbolic]] and [[Real]], and the [[subject]] to each, in a way which avoids any [[notion ]] of hierarchy, or any priority of any one of the three terms.)