Page 215 - J. C. Turner - History and Science of Knots

CHAPTER 11

A HISTORY OF TOPOLOGICAL KNOT THEORY

Pieter van de Griend

The subject is a very much more
difficult and intricate one than at
first sight one is inclined to think.
Peter Guthrie Tait, 1876.

1. Introduction
In this Chapter, knot theory will be used as a generic term to signify what
mathematicians often distinguish into two separate theories , the one concerned
with n-links and the other dealing with braids. To a mathematician a knot is
a single closed curve that meanders smoothly through Euclidean three-space
without intersecting itself. An n-link is composed of n of such components,
which may link and intertangle but not intersect each other. This affords a
simple and intuitive picture, capturing the most essential aspects of a real-life
knotted structure . The mathematical concept of a braid will be treated in a
later section.
Any account of the history of mathematical knot theory inevitably will be
fragmented over many aspects of the fields across which the subject stretches.
Combinatorics, topology and group theory are but a few of these fields. In
this exposition I have chosen to give a broad outline which touches upon the
main conceptual developments as seen in an historic perspective, in which the
more formal theoretical developments feature in the background . Knot theory
has now become a subject in its own right, which has grown by leaps and

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