Tree diagrams for string links II: Determining chord diagrams

Blake Mellor

doi:10.1142/S0218216508006336

Tree diagrams for string links II: Determining chord diagrams

Blake Mellor

Mathematics, Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

Abstract

In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).

Original language	English
Pages (from-to)	649-664
Number of pages	16
Journal	Journal of Knot Theory and its Ramifications
Volume	17
Issue number	6
DOIs	https://doi.org/10.1142/S0218216508006336
State	Published - Jun 2008

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Chord diagrams
Finite type invariants
Intersection graphs
String links

Disciplines

Discrete Mathematics and Combinatorics
Geometry and Topology

Access to Document

10.1142/S0218216508006336

https://digitalcommons.lmu.edu/math_fac/33

Cite this

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title = "Tree diagrams for string links II: Determining chord diagrams",

abstract = " In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).",

keywords = "Chord diagrams, Finite type invariants, Intersection graphs, String links",

author = "Blake Mellor",

note = "Mellor, B., 2008: Tree Diagrams for String Links II: Determining Chord Diagrams. J. Knot Theory Ramif., 17.6, 649-664, arXiv:math/0408286.",

year = "2008",

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language = "English",

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journal = "Journal of Knot Theory and its Ramifications",

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N2 - In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).

AB - In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).

KW - Chord diagrams

KW - Finite type invariants

KW - Intersection graphs

KW - String links

U2 - 10.1142/S0218216508006336

DO - 10.1142/S0218216508006336

M3 - Article

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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