0 1

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0 1.gif


3 1.gif


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 0 1 at Knotilus!

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
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]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
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)
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

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n34, K11n42,}

Same Jones Polynomial (up to mirroring, ): {}

Vassiliev invariants

V2 and V3: (0, 0)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 0 is the signature of 0 1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.    Data:0 1/KhovanovTable
Integral Khovanov Homology

(db, data source)

   Data:0 1/Integral Khovanov Homology

The Coloured Jones Polynomials