On Two Categorifications of the Arrow Polynomial for Virtual Knots

Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to infinitely many variables, each variable corresponding to an integer arrow number calculated from each loop in an oriented state summation for the bracket. The categorifications are based on new gradings associated with these arrow numbers, and give homology theories associated with oriented virtual knots and links via extra structure on the Khovanov chain complex. Applications are given to the estimation of virtual crossing number and surface genus of virtual knots and links.

Авторы
Dye H.A.1 , Kauffman L.H.2 , Manturov V.O. 3
Редакторы
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Сборник статей
Издательство
SPRINGER-VERLAG BERLIN
Номер выпуска
-
Язык
Английский
Страницы
95-124
Статус
Опубликовано
Подразделение
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Ссылка
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Номер
-
Том
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Год
2011
Организации
  • 1 McKendree Univ, Div Sci & Math, Lebanon, IL 62254 USA
  • 2 Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
  • 3 Peoples Friendship Univ Russia, Moscow 117198, Russia
Ключевые слова
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Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/8562/