Quantum Groups pp 241-274 | Cite as

Knots, Links, Tangles, and Braids

Part of the Graduate Texts in Mathematics book series (GTM, volume 155)


We now embark into a topological digression which will lead us into the world of knots. The reason for the presence of this chapter in a book de-voted to quantum groups is the close relationship between the newly dis-covered invariants of links (such as the celebrated Jones polynomial) and R-matrices. This relationship will become more precise in Chapter XII. In this one we proceed to describe several classes of one-dimensional subman-ifolds of the three-dimensional space R3, such as knots, links, tangles, and braids. Since there are excellent textbooks on knot theory, we shall not prove all assertions that can be found elsewhere. Nevertheless, all results pertaining to the matter of this book, namely those connecting topological problems with the algebra of quantum groups, will be proved in detail.


Fundamental Group Braid Group Isotopy Class Reidemeister Move Link Diagram 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur-C.N.R.S.StrasbourgFrance

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