Tony Hughes – Lacan’s Use of Topology – A Chronology

The Letter 59 & 60 Summer – Autumn 2015, pages 91-105

Lacan’s use of topology seems to have begun with the Rome Discourse in September
1953. From that time on until the end of his life he used it extensively
throughout his seminars, and perhaps in other areas of his work. This paper
sets out chronologically the occasions from 1953 to 1955 where he referred
to topology either directly or indirectly. It also attempts to give some insights
into how space is conceived in topology. That Lacan’s work is mostly done by
reference to types of space that are different to that of Euclid is essential to
our reading of Lacan. Some aspects of this space are discussed, as well as the
link between the work of Lévi- Strauss and topology.
Keywords: topology, Moebian space, the projective plane, Granon-Lafont,
bosons and fermions, the cross-cap, the Moebius strip.
Introduction
It is hard to define the precise point at which I got hooked by Lacan’s work
on topology. It is possible to highlight a certain moment in L’Etourdit, where,
at the start of the Second Turn, Lacan describes some aspects of his topology.
These sections on topology are hard to follow, because Lacan deliberately
avoids the use of diagrams. However, this lack was compensated for to some
extent, by virtue of Fieren’s Reading L’Etourdit (2002).  His use of diagrams
of the torus, Moebius strip, Klein bottle and the cross-cap, provided some
clarification. As I began to delve more deeply into the topic, I became aware
of a question – when did topology begin in Lacan’s work? Consequently
I consulted Krutzen’s Index which details many of the various topics in
Lacan’s seminars. …

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