K11a61

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K11a60.gif

K11a60

K11a62.gif

K11a62

K11a61.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11a61 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8394 X16,6,17,5 X10,8,11,7 X2,9,3,10 X18,12,19,11 X20,14,21,13 X6,16,7,15 X22,18,1,17 X14,20,15,19 X12,22,13,21
Gauss code 1, -5, 2, -1, 3, -8, 4, -2, 5, -4, 6, -11, 7, -10, 8, -3, 9, -6, 10, -7, 11, -9
Dowker-Thistlethwaite code 4 8 16 10 2 18 20 6 22 14 12
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11a61 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a61/ThurstonBennequinNumber
Hyperbolic Volume 14.3183
A-Polynomial See Data:K11a61/A-polynomial

[edit Notes for K11a61's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for K11a61's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 103, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11a61/QuantumInvariant/A2/1,0
The G2 invariant Data:K11a61/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

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

Vassiliev invariants

V2 and V3: (2, 5)
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 2 is the signature of K11a61. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-2-10123456789χ
21           1-1
19          2 2
17         41 -3
15        62  4
13       84   -4
11      86    2
9     88     0
7    78      -1
5   48       4
3  37        -4
1 15         4
-1 2          -2
-31           1
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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K11a60.gif

K11a60

K11a62.gif

K11a62