Fibred knots and virtual knots

We introduce a new technique for studying classical knots with the methods of virtual knot theory. Let K be a knot and J be a knot in the complement of K with lk(J, K) = 0. Suppose there is covering space $\piJ : \Sigma \times (0, 1) \to \overline{S3 \backslash V(J)}$, where V(J) is a regular neighborhood of J satisfying V(J) ∩ im(K) = ∅ and Σ is a connected compact orientable 2-manifold. Let K′ be a knot in Σ × (0, 1) such that πJ(K′) = K. Then K′ stabilizes to a virtual knot $\hat{K}$, called a virtual cover of K relative to J. We investigate what can be said about a classical knot from its virtual covers in the case that J is a fibered knot. Several examples and applications to classical knots are presented. A basic theory of virtual covers is established. © 2013 World Scientific Publishing Company.

Авторы
Chrisman M.W.1 , Manturov V.O. 2
Редакторы
-
Издательство
-
Номер выпуска
12
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
1341003
Том
22
Год
2013
Организации
  • 1 Monmouth University, West Long Branch, NJ,07764, United States
  • 2 Peoples' Friendship University of Russia, Miklukho-Maklay Street 6, Moscow 117198, Russian Federation
Ключевые слова
Applications of virtual knot theory; Covering; Fibered knot; Parity; Virtual knot
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/1996/