FREE KNOTS AND GROUPS-Reference-Cited by-同舟云学术

FREE KNOTS AND GROUPS

Published:2010-02 Issue:02 Volume:19 Page:181-186
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

MANTUROV O. V.,MANTUROV V. O.¹

Affiliation:

1. People's Friendship University of Russia, Faculty of Sciences, 3 Ordjonikidze St., Moscow, 117923, Russia

Abstract

Free knots are a simplification of virtual knots obtained by forgetting arrow/sign information at classical crossings. First non-trivial examples of free knots were constructed recently by the second named author. By using parity considerations, we construct invariants of free knots valued in certain groups. These groups have a simple combinatorial description, the first one being the infinite dihedral group.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216510007826

Reference4 articles.

1. Topology of words

2. V. O. Manturov, Knot Theory (Chapman and Hall/CRC, 2005) p. 416.

3. INTRODUCTION TO GRAPH-LINK THEORY

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A free-group valued invariant of free knots;Journal of Knot Theory and Its Ramifications;2021-05

2. Combinatorial random knots;Involve, a Journal of Mathematics;2020-11-20

3. A family of polynomial invariants for flat virtual knots;Topology and its Applications;2019-09

4. The three loop isotopy and framed isotopy invariants of virtual knots;Topology and its Applications;2014-08

5. Parity in knot theory and graph-links;Journal of Mathematical Sciences;2013-08-29