Download E-books A Study of Braids (Mathematics and Its Applications) PDF

By Kunio Murasugi

In bankruptcy 6, we describe the idea that of braid equivalence from the topological viewpoint. it will lead us to a brand new notion braid homotopy that's mentioned totally within the subsequent bankruptcy. As simply pointed out, in bankruptcy 7, we will talk about the variation among braid equivalence and braid homotopy. additionally during this bankruptcy, we outline a homotopy braid invariant that seems to be the so-called Milnor quantity. bankruptcy eight is a brief evaluate of knot thought, together with Alexander's theorem. whereas, Chapters nine is dedicated to Markov's theorem, which permits the applying of this conception to different fields. This was once one of many motivations Artin had in brain whilst he started learning braid idea. In bankruptcy 10, we talk about the first functions of braid concept to knot conception, together with the advent of crucial invariants of knot thought, the Alexander polynomial and the Jones polynomial. In bankruptcy eleven, influenced by means of Dirac's string challenge, the normal braid team is generalized to the braid teams of assorted surfaces. We talk about those teams from an intuitive and diagrammatic viewpoint. within the final brief bankruptcy 12, we current with out evidence one theorem, because of Gorin and Lin [GoL] , that could be a dazzling program of braid thought to the idea of algebraic equations.

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