Чистая математика и смежные философские проблемы.
In recent years braid groups are intensively studied, in
particular, there is well-known result by Thurston, that these
Groups admit biautomatic structure, that yields to normal forms in
braids. Unfortunately, these normal forms are very dull from
computational point of view and are inconvenient to use in
applications.
© 1996-2002, Сибирское отделение Российской академии наук, Новосибирск
Recall, that Artin braid group on $n+1$ strands is a group given
with the following generators and relations:
begin{equation} label{eq:B}
B_{n+1}= left
We find new normal forms for braids, which possess extremely
natural geometric description.
The main geometric idea of our normal form is to pull down-right
the third strand, lowering it till possible. This process allows
us to have all crossings that involve first and second strand in
the very left upper corner. And the the crossings that involve
strands with bigger number lower.
We introduce a new order on $B_{n+1}$ and Knuth-Bendix (or
Grobner-Shirshov) type algorithm, that by given braid word
calculates its normal form, which turns out to be the least in the
sense of our order.
Ваши комментарии
Обратная связь
[Головная страница]