Abstract
We show how to derive a theory of (infinite) braids which includes the well known classical theory of braids due to Emil Artin. We use this theory to give a theory of (infinite) knots which includes the classical theory of knots. A vital role in the new theory is played by the topological free group which was first defined and studied by Graham Higman. This is only a preliminary attempt to extend the classical theory. As we make use of a somewhat intuitive approach to the subject, we leave a number of basic problems still outstanding. We assume that the reader is familiar with the theory of braids and knots as given in E. Artin [1], J.S. Birman [2] and S. Moran [5]. We also make use of the fact that the fundamental group of a certain region in R 2 is a topological free group as given in G. Higman [4], H.B. Griffiths [3], J.W. Morgan and I.A. Morrison [6].
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