Parity and cobordism of free knots

A simple invariant is constructed which obstructs a free knot to be truncated. In particular, this invariant provides an obstruction to the truncatedness of curves immersed in two-dimensional surfaces. A curve on an oriented two-dimensional surface S g is referred to as truncated (nullcobordant) if there exists a three-dimensional manifold M with boundary S g and a smooth proper map of a two-disc to M such that the image of the boundary of the disc coincides with the curve. The problem of truncatedness for free knots is solved in this paper using the notion of parity recently introduced by the author. © 2012 RAS(DoM) and LMS.

Авторы
Редакторы
-
Журнал
Издательство
Russian Academy of Sciences
Номер выпуска
2
Язык
Английский
Страницы
196-223
Статус
Опубликовано
Подразделение
-
Номер
-
Том
203
Год
2012
Организации
  • 1 University of Russia, Moscow, Russian Federation
Ключевые слова
Cobordism; Free knot; Knot; Parity; Surface
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/2327/