Parity, free knots, groups, and invariants of finite type

In this paper, on the basis of the notion of parity introduced recently by the author, for each positive integer m we construct invariants of long virtual knots with values in some simply defined group Gm; conjugacy classes of this group play a role as invariants of compact virtual knots. By construction, each of the invariants is unaltered by the move of virtualization. Factorization of the group algebra of the corresponding group leads to invariants of finite order of (long) virtual knots that do not change under virtualization. The central notion used in the construction of the invariants is parity: the crossings of diagrams of free knots is endowed with an additional structure — each crossing is declared to be even or odd, where even crossings behave regularly under Reidemeister moves. © 2012 American Mathematical Society.

Авторы
Редакторы
-
Издательство
American Mathematical Society
Номер выпуска
-
Язык
Английский
Страницы
157-169
Статус
Опубликовано
Подразделение
-
Номер
-
Том
72
Год
2011
Организации
  • 1 People’s Friendship University, Moscow, Russian Federation
Ключевые слова
Free knot; Group; Invariant; Invariant of finite order; Knot; Parity; Virtual knot
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/2606/