The group of parenthesized braids
- 作者：Patrick Dehornoy
- 关键词：Thompson's groups ; Coxeter relations ; Braid groups ; Mapping class group ; Cantor set ; Automorphisms of a free group ; Orderable group ; Group of fractions ; Word reversing
- 刊名：Advances in Mathematics
- 出版年：2006
- 期刊代码：62_00018708
- 类别：mt
- 出版时间：1 October 2006
- 卷：205
- 期：2
- 页码：354-409
- 文件大小：612 K
摘要
We investigate a group me="mml1">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml1&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=8d34d61dfa447c8f71e5b4bc3830707e" title="Click to view the MathML source">Bb>• b> that includes Artin's braid group me="mml2">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml2&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=3fbdbc23dae4a1bc3bf3d8683eee1a57" title="Click to view the MathML source">Bb>∞ b> and Thompson's group F. The elements of me="mml3">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml3&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=f182228679e10dbc7da85af7a2c99801" title="Click to view the MathML source">Bb>• b> are represented by braids diagrams in which the distances between the strands are not uniform and, besides the usual crossing generators, new rescaling operators shrink or stretch the distances between the strands. We prove that me="mml4">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml4&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=fc09b991add267bb199b4f43fbbe443a" title="Click to view the MathML source">Bb>• b> is a group of fractions, that it is orderable, admits a nontrivial self-distributive structure, i.e., one involving the law me="mml5">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml5&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=894a8eba8de9dfd16be1db8430749af1" title="Click to view the MathML source">x(yz)=(xy)(xz), it embeds in the mapping class group of a sphere with a Cantor set of punctures, and that Artin's representation of me="mml6">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml6&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=07776433c100a4a9fdebb5b55cf483e0" title="Click to view the MathML source">Bb>∞ b> into the automorphisms of a free group extends to me="mml7">black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6W9F-4H57JT4-1&_mathId=mml7&_user=10&_cdi=6681&_rdoc=4&_handle=V-WA-A-W-AA-MsSAYWB-UUA-U-AAZCWBYECE-AAZWYAEDCE-VWBVAVDD-AA-U&_acct=C000050221&_version=1&_userid=10&md5=ec7a595475186d2c99790099ac7f0bee" title="Click to view the MathML source">Bb>• b>.