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(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n19 at Knotilus!

Knot presentations

Planar diagram presentation X4251 X8394 X10,6,11,5 X7,17,8,16 X2,9,3,10 X11,18,12,19 X13,20,14,21 X15,22,16,1 X17,7,18,6 X19,12,20,13 X21,14,22,15
Gauss code 1, -5, 2, -1, 3, 9, -4, -2, 5, -3, -6, 10, -7, 11, -8, 4, -9, 6, -10, 7, -11, 8
Dowker-Thistlethwaite code 4 8 10 -16 2 -18 -20 -22 -6 -12 -14
A Braid Representative
A Morse Link Presentation K11n19 ML.gif

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 2

[edit Notes for K11n19's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 5, -4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant Data:K11n19/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n135,}

Same Jones Polynomial (up to mirroring, ): {4_1,}

Vassiliev invariants

V2 and V3: (-1, 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 -4 is the signature of K11n19. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
j \
5       11
3        0
1     11 0
-1   11   0
-3   11   0
-5 111    1
-7        0
-911      0
Integral Khovanov Homology

(db, data source)


Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages.

See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

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