CUBE DIAGRAMS AND 3-DIMENSIONAL REIDEMEISTER-LIKE MOVES FOR KNOTS-Reference-Cited by-同舟云学术

CUBE DIAGRAMS AND 3-DIMENSIONAL REIDEMEISTER-LIKE MOVES FOR KNOTS

Published:2012-04 Issue:05 Volume:21 Page:1250033
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

BALDRIDGE SCOTT¹,LOWRANCE ADAM M.²

Affiliation:

1. Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana, 70803, USA

2. Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242, USA

Abstract

In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is invariant under five cube diagram moves. A knot homology is constructed from cube diagrams and shown to be equivalent to knot Floer homology.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216511009832

Reference8 articles.

1. H. Brunn, Verhandlungen des Internationalen Mathematics Kongresses (Zurich, 1897) pp. 256–259.

2. M. Dehn and P. Heegaard, Analysis Situs, Encyklopädie der Mathematischer Wissenschajten III (Teubner, Leipzig, 1907) pp. 153–220.

3. Embedding knots and links in an open book I: Basic properties

4. Arc-presentations of links: Monotonic simplification

Cited by 4 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. Yarn ball knots and faster computations;Journal of Applied and Computational Topology;2023-10-28

2. Lifting Lagrangian immersions in ℂPn−1 to Lagrangian cones in ℂn;Open Book Series;2022-10-27

3. On the rotation class of knotted Legendrian tori in R5;Topology and its Applications;2016-08

4. CUBULATED MOVES AND DISCRETE KNOTS;Journal of Knot Theory and Its Ramifications;2013-12