Subject: a question
From: Joan Birman <jb@cpw.math.columbia.edu>
Date: Sat, 4 Nov 2006 15:04:56 -0500 (EST)

I have a question for your mailing list:

In 1953 H. Schubert published his seminal paper, "Knoten und Vollringe", 
in Acta Math {\bf 90}, 131-286. The paper is long and very detailed, and 
quite difficult to read. It has come up many times during the past years, 
e.g. recently a student asked me whether a type (p,q) torus knot, p<q, has 
a unique conjugacy class of p-braid representatives. Schubert's paper is 
the correct reference, yet it's a poor one because the needed result is 
near the end of his 155 page paper and is almost impossible to pinpint 
without wading through many pages of definitions and theorems which are 
aimed at more general results about companion knots, where the needed case 
might well turn out to be exceptional because a torus knot is a cable on 
the unknot and in some of the preliminary lemmas one sees the 
qualification "non-trivial knot". Does anyone know of related review 
articles or textbook discussions or summaries of Schubert's paper?

Sincerely,
Joan Birman