# Template:Rolfsen Knot Page

This is the Rolfsen Knot Page master template. For testing purposes, some of the data in it is filled in with data for 8_17.

 (KnotPlot image) See the full Rolfsen Knot Table. Visit Rolfsen Knot Page's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit Rolfsen Knot Page at Knotilus!

### Knot presentations

Minimum Braid Representative A Morse Link Presentation An Arc Presentation

Length is 8, width is 3,

Braid index is 3

[{7, 10}, {9, 2}, {10, 4}, {3, 5}, {4, 8}, {6, 9}, {5, 1}, {2, 7}, {1, 6}, {8, 3}]

### Three dimensional invariants

 Symmetry type Data:Rolfsen Knot Page/Symmetry Type Unknotting number Data:Rolfsen Knot Page/Unknotting Number 3-genus Data:Rolfsen Knot Page/3-Genus Bridge index Missing Super bridge index Missing Nakanishi index Missing Maximal Thurston-Bennequin number Data:Rolfsen Knot Page/ThurstonBennequinNumber Hyperbolic Volume Data:Rolfsen Knot Page/HyperbolicVolume A-Polynomial See Data:Rolfsen Knot Page/A-polynomial

### Four dimensional invariants

 Smooth 4 genus Missing Topological 4 genus Missing Concordance genus Missing Rasmussen s-Invariant Missing

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

Same Alexander/Conway Polynomial: {{{{same_alexander}}}}

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

### Vassiliev invariants

 V2 and V3: (Data:Rolfsen Knot Page/V 2, Data:Rolfsen Knot Page/V 3)
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 Data:Rolfsen Knot Page/V 2,1 Data:Rolfsen Knot Page/V 3,1 Data:Rolfsen Knot Page/V 4,1 Data:Rolfsen Knot Page/V 4,2 Data:Rolfsen Knot Page/V 4,3 Data:Rolfsen Knot Page/V 5,1 Data:Rolfsen Knot Page/V 5,2 Data:Rolfsen Knot Page/V 5,3 Data:Rolfsen Knot Page/V 5,4 Data:Rolfsen Knot Page/V 6,1 Data:Rolfsen Knot Page/V 6,2 Data:Rolfsen Knot Page/V 6,3 Data:Rolfsen Knot Page/V 6,4 Data:Rolfsen Knot Page/V 6,5 Data:Rolfsen Knot Page/V 6,6 Data:Rolfsen Knot Page/V 6,7 Data:Rolfsen Knot Page/V 6,8 Data:Rolfsen Knot Page/V 6,9

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 ${\displaystyle t^{r}q^{j}}$ 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 ${\displaystyle s=}$Data:Rolfsen Knot Page/Signature is the signature of Rolfsen Knot Page. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. Data:Rolfsen Knot Page/KhovanovTable