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A Primer on Mapping Class Groups (PMS-49) by Dan Margalit, Benson Farb

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Chapter Nine

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Braid Groups

In this chapter we give a brief introduction to Artin’s classical braid groups Bn. While Bn is just a special kind of mapping class group, namely, that of a multipunctured disk, the study of Bn has its own special flavor. One reason for this is that multipunctured disks can be embedded in the plane, so that elements of Bn lend themselves to specialized kinds of pictorial representations.

9.1 THE BRAID GROUP: THREE PERSPECTIVES

The notion of a mathematical braid is quite natural and classical. For instance, this concept appeared in Gauss’s study of knots in the early nineteenth century (see [182]) and in Hurwitz’s 1891 ...

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