On complexity of the word problem in braid groups and mapping class groups
نویسندگان
چکیده
منابع مشابه
From braid groups to mapping class groups
This paper is a survey of some properties of the braid groups and related groups, that lead to questions on mapping class groups. AMS Subject Classification: Primary 20F36. Secondary 57M99, 57N05.
متن کاملDelta-structures on mapping class groups and braid groups
We describe a Delta-group structure on the mapping class groups of surfaces, and show that it is compatible with the Delta-group structures of the braid groups of surfaces given by Berrick-Cohen-Wong-Wu. We then prove an isomorphism theorem relating these two Delta-groups. This is the first of a pair of papers on this topic.
متن کاملBrunnian subgroups of mapping class groups and braid groups
In this paper we continue our study of the Delta-group structure on the braid groups and mapping class groups of a surface. We calculate the homotopy groups of these Delta-groups and prove some results about Brunnian braid groups and Brunnian mapping class groups. This is the second of a pair of papers on these structures.
متن کاملTwisted Conjugacy Classes in Symplectic Groups, Mapping Class Groups and Braid Groups
We prove that the symplectic group Sp(2n,Z) and the mapping class group ModS of a compact surface S satisfy the R∞ property. We also show that Bn(S), the full braid group on n-strings of a surface S, satisfies the R∞ property in the cases where S is either the compact disk D, or the sphere S. This means that for any automorphism φ of G, where G is one of the above groups, the number of twisted ...
متن کاملAn algorithm for the word problem in braid groups
We suggest a new algorithm for finding a canonical representative of a given braid, and also for the harder problem of finding a σ1 consistent representative. We conjecture that the algorithm is quadratictime. We present numerical evidence for this conjecture, and prove two results: (1) The algorithm terminates in finite time. (2) The conjecture holds in the special case of 3-string braids in f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2000
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00063-2