(Progress in Mathematics) Patrick Dehornoy-Braids and Self-Distributivity -Birkh盲user Basel (2000).pdf
Contents Preface vii Part A: Ordering the Braids I. Braids vs. Self-Distributive Systems 1 Braid Groups ....................... 4 Braid Colourings ......................13 A Self-Distributive Operation on Braids ............26 Extended Braids ......................35 Notes ...........................44 II. Word Reversing 47 Presentations ................48 plements ...................58 Garside Elements .....................68 The Case of Braids .....................78 Double Reversing .....................87 Notes ..........................94 III. The Braid Order 97 More about Braid Colourings ................98 The Linear Ordering of Braids .............. 106 Handle Reduction .................... 115 Alternative Definitions .................. 127 Notes ......................... 137 iv Contents IV. The Order on Positive Braids 141 The Case of Three Strands ................ 142 The General Case .................... 150 Applications ...................... 165 Notes ......................... 170 : Rank Tables ................... 172 Part B: Free LD-systems V. Orders on Free LD-systems 175 Free Systems ...................... 178 The Absorption Property ................. 186 The Confluence Property ................. 193 parison Property ................ 200 Canonical Orders .................... 209 Applications ....................... 216 Notes .......................... 231 VI. Normal Forms 235 Terms as Trees ..................... 236 The Cuts of a Term ................... 242 The ∂-Normal Form ................... 250 The Right Normal Form ................. 256 Applications ...................... 271 Notes ......................... 276 : The First Codes ................. 280 VII. The Geometry Monoid 2
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