Question about Alexander and Briggs notation

  • Context: Graduate 
  • Thread starter Thread starter ComputerGeek
  • Start date Start date
  • Tags Tags
    Notation
Click For Summary
SUMMARY

The discussion centers on the Alexander and Briggs notation used in Knot Theory, specifically regarding the classification of knots based on their crossings. The user seeks clarification on the notation, particularly the significance of the superscripts and subscripts in the context of knot classification. It is confirmed that the superscripts indicate the number of components in a link, while the subscripts represent a historical ordering of knots. The Knot Atlas is recommended as a resource for further exploration of knot tables.

PREREQUISITES
  • Understanding of Knot Theory concepts
  • Familiarity with Alexander and Briggs notation
  • Knowledge of Reidemeister moves
  • Basic grasp of knot classification and crossings
NEXT STEPS
  • Research the significance of superscripts in knot notation
  • Explore the Knot Atlas for comprehensive knot tables
  • Study the implications of historical ordering in knot classification
  • Learn more about the classification of knots with 8 fundamental crossings
USEFUL FOR

Students and researchers in geometry, particularly those studying Knot Theory, as well as anyone interested in the classification and notation of knots.

ComputerGeek
Messages
383
Reaction score
0
I am writing a small paper on Knot Theory for my undergrad geometry course and I have a question about the tabulation of knots.

The books I have discuss the different notations, except for the ALexander and Briggs notation, which is used in the tables provided in the appendices.

I believe I understand the notation, but I want to be sure.

4_1 which refers to the figure eight knot means that this is the first knot of the class of knots that has 4 crossings that cannot be undone by Reidemeister moves. correct? If that is the case, then in the set of knots with 8 fundamental crossings, is there any significance to their ordering in the table? could I take 8_1 and 8_2 and just switch their corresponding knots? also, on some of the knots, there is a superscript. what is the significance of that?

Thanks.
 
Physics news on Phys.org
In my book (Adams), the superscripts refer to the number of components in the link. I think the subscript is just a historical ordering. For more tables, see the Knot Atlas.
 

Similar threads

Graduate Question about an equation from anapole measurement paper
  • · Replies 1 ·
Replies
1
Views
1K
Graduate A question about notation on derivatives
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Questions about tangent spaces & the tangent bundle
  • · Replies 11 ·
Replies
11
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 261)
  • · Replies 5 ·
Replies
5
Views
3K
Admissions Could I please get critique on my SOP? (Experimental Biophysics)
  • · Replies 8 ·
Replies
8
Views
911
Graduate Feeling uncomfortable about Wick-rotations
  • · Replies 18 ·
Replies
18
Views
5K
Schools Some questions about applying to graduate school
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Some questions about Cosmic Microwave Background radiation
  • · Replies 13 ·
Replies
13
Views
6K
Undergrad The standard model from loop quantum gravity via spinors octonions
  • · Replies 26 ·
Replies
26
Views
5K
About to Graduate in the UK - Questions on UK+EU Masters
  • · Replies 4 ·
Replies
4
Views
2K