Abstract
If a is a braid with n components, the closure of a, denoted #, is constructed by connecting the endpoints at the top level to the bottom endpoints with n standard curves. This procedure yields an oriented link ~ having the same number of crossings as a. A classical result of Alexander [I], [2], [3] states that every oriented link is isotopic to a closed braid #. In his proof Alexander modifies the diagram of an oriented link by a sequence of elementary operations to obtain a closed braid. During this transformation the geometry of the picture is completely changed. In many applications of Alexander's algorithms links with few crossings yield closed braid with a large number of crossings. On the other hand many algebraic invariants of links are first defined on braids. If we wish to compute these invariants for a small link L, it will be very useful to have the following principle:
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