Notice. The Knot Atlas is now recovering from a major crash. Hopefully all functionality will return slowly over the next few days. --Drorbn (talk) 21:23, 4 July 2013 (EDT)

0 1

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0 1.gif

0_1

3 1.gif

3_1

Contents

0 1.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 0 1's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit \textrm{KnotilusURL}(\textrm{GaussCode}()) at Knotilus!

Visit 0 1's page at the original Knot Atlas!

Also known as "the Unknot"


A temple symbol MANJI in a Japanese map[1]
A toroidal bubble in glass [2]
Simple closed loop as pseudo-knot
Emblem of Fukuoka prefecture, Japan
Elaborate heraldic depiction
Ornamentation in Palermo, Sicily

Knot presentations

Planar diagram presentation \textrm{Loop}(1)
Gauss code
Dowker-Thistlethwaite code
Conway Notation Data:0 1/Conway Notation


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
Data:0 1/BraidPlot
Length is Data:0 1/MinimalBraidLength, width is Data:0 1/MinimalBraidWidth,

Braid index is Data:0 1/BraidIndex

0 1 ML.gif 0 1 AP.gif
[{1, 2}, {2, 1}]

[edit Notes on presentations of 0 1]


Three dimensional invariants

Symmetry type
Unknotting number 0
3-genus 0
Bridge index 1
Super bridge index
Nakanishi index
Maximal Thurston-Bennequin number [-1][-1]
Hyperbolic Volume Data:0 1/HyperbolicVolume
A-Polynomial See Data:0 1/A-polynomial

[edit Notes for 0 1's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus \textrm{ConcordanceGenus}(\textrm{Knot}(0,1))
Rasmussen s-Invariant Missing

[edit Notes for 0 1's four dimensional invariants]

Polynomial invariants

Alexander polynomial 1
Conway polynomial 1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 1, 0 }
Jones polynomial 1
HOMFLY-PT polynomial (db, data sources) 1
Kauffman polynomial (db, data sources) 1
The A2 invariant Data:0 1/QuantumInvariant/A2/1,0
The G2 invariant q^{10}+q^8+q^2+1+ q^{-2} + q^{-8} + q^{-10}