Garside Theory on Reducible Braids
نویسنده
چکیده
The braid group Bn is the mapping class group of an n-punctured disk. An n-braid is reducible if it has an invariant essential curve system in the punctured disk. We show that for some class of reducible braids (including split braids), finding a reduction system is as easy as finding one element in the ultra summit set.
منابع مشابه
A Garside-theoretic Approach to the Reducibility Problem in Braid Groups Eon-kyung Lee and Sang
Let Dn denote the n-punctured disk in the complex plane, where the punctures are on the real axis. An n-braid α is said to be reducible if there exists an essential curve system C in Dn, called a reduction system of α, such that α ∗ C = C where α ∗ C denotes the action of the braid α on the curve system C. A curve system C in Dn is said to be standard if each of its components is isotopic to a ...
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