# 0 1

 (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 ${\displaystyle {\textrm {Loop}}(1)}$ 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/BraidPlotLength is Data:0 1/MinimalBraidLength, width is Data:0 1/MinimalBraidWidth, [{1, 2}, {2, 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

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial 1 Conway polynomial 1 2nd Alexander ideal (db, data sources) ${\displaystyle \{1\}}$ 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 ${\displaystyle q^{10}+q^{8}+q^{2}+1+q^{-2}+q^{-8}+q^{-10}}$

### "Similar" Knots (within the Atlas)

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

Same Jones Polynomial (up to mirroring, ${\displaystyle q\leftrightarrow q^{-1}}$): {}

### 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 ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$ ${\displaystyle ?}$

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 ${\displaystyle t^{r}q^{j}}$ are shown, along with their alternating sums ${\displaystyle \chi }$ (fixed ${\displaystyle j}$, alternation over ${\displaystyle r}$). The squares with yellow highlighting are those on the "critical diagonals", where ${\displaystyle j-2r=s+1}$ or ${\displaystyle j-2r=s-1}$, where ${\displaystyle s=}$0 is the signature of 0 1. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. Data:0 1/KhovanovTable