Page 222 - J. C. Turner "History and Science of Knots"

A History of Topological Knot Theory 213

length the value of the above-mentioned integral [18]. He later expanded this
work to illustrate the connection between knots and Riemann surfaces [19, p.
316]. A diagram from one of Boedicker's papers is shown in Fig. 5.
In any case, Gauss' knotting attempts made him (Gauss) conscious of the
semantic difficulties continually to be found in topological studies. This placed
him among the first to display, and encourage, deep scientific and mathemat-
ical interest in knotted structures. Gauss certainly led some of his students
to study the intricacies of topology. Fortunately one of them, Johann Listing,
was inspired to pursue vigorously the quest for knot knowledge. He thereby
secured for himself a name amongst the founders of the subject. Through his
work, which we describe next, the roots of the family tree of modern knot
theory are firmly anchored in nineteenth century mathematics.

4. Johann Listing's Complexions-Symbol

Johann Benedict Listing (1806-82) was a student of Gauss in 1834 who later
became professor of physics at Gottingen. His topological researches eventually
led him to publish some of his work on knots in an essay entitled Vorstudien
ziir Topologie, in 1847 [62]. In this work he discussed what he preferred to call
the geometry of position, but since this term had been reserved for projective
geometry by von Staudt, he used the term topology instead. This became the
collective name for the mathematical disciplines which study the more general
concepts of geometric structures. Listing, even though he carried out quite
considerable work on the subject, seems to have published a mere fraction of
these researches. *

Fig. 6. Handedness of Oriented Crossings
In his 1847 publication he considered the handedness of spirals and dis-
cerned between their ability to be either left- or right-handed, which he termed
respectively dexiotropy and laeotropy. Planar projections of these spirals led

*Letter by Listing to the Proc. Roy. Soc. Edinburgh (1877). p. 316.