38899

Автор(ы): 

Автор(ов): 

3

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

On Marked Braid Groups

ISBN/ISSN: 

0218-2165

Наименование источника: 

  • Journal of Knot Theory and Its Ramifications

Обозначение и номер тома: 

Vol. 24, No. 13

Город: 

  • Singapore

Издательство: 

  • World Scientific Publishing Company

Год издания: 

2015

Страницы: 

1541005 (12 pages)
Аннотация
In the present paper, we introduce Z2-braids and, more generally, G-braids for an arbitrary group G. They form a natural group-theoretic counterpart of G-knots, see [2]. The underlying idea, used in the construction of these objects — decoration of crossings with some additional information — generalizes an important notion of parity introduced by the second author (see [1]) to different combinatorically–geometric theories, such as knot theory, braid theory and others. These objects act as natural enhancements of classical (Artin) braid groups. The notion of dotted braid group is introduced: classical (Artin) braid groups live inside dotted braid groups as those elements having presentation with no dots on the strands. The paper is concluded by a list of unsolved problems.

Библиографическая ссылка: 

Мантуров В.О., Федосеев Д.А., Cheng Z. On Marked Braid Groups // Journal of Knot Theory and Its Ramifications. 2015. Vol. 24, No. 13. С. 1541005 (12 pages).