My main mathematical research interests are in topology, algebra, geometry and dynamics. I have a particular interest in the theory of knots, and my book, "Knots and Links," is a standard reference and textbook on the subject. A new edition of this book is published by the American Mathematical Society in the Chelsea series
In recent years I have concentrated on algebraic aspects of topology, in particular orderable groups and their applications. This interest was sparked by the discovery by Dehornoy that the so-called Braid groups are left-orderable groups. An account of this phenomenon appears in the book Why are braids orderable? published in the "Panoramas et synthese" series of the Soc. Math. France. by Dehornoy, Dynnikov, Rolfsen and Wiest. An updated version, by the same authors, is published by the American Mathematical Society series of Mathematical Surveys and Monographs, called Ordering braids .
Fundamental groups of 3-manifolds also have interesting orderability properties, which are intimately connected with structures such as fibrations and foliations of the 3-manifold. This is one of the focal points of my current research.
Some of my recent papers, lecture notes and preprints are available in PDF form. A list of these, with abstracts, can be found by clicking HERE .
PostScript files can be read by Acrobat Reader, which can be downloaded free.