{{Rolfsen Knot Page| n = 10 | k = 132 | KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-3,9,10,-2,-5,6,-9,3,-7,8,-4,5,-6,4,-8,7/goTop.html | braid_table =
[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]
[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]
[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]
[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]
| braid_crossings = 11 | braid_width = 4 | braid_index = 4 | same_alexander = [[5_1]], | same_jones = [[5_1]], | khovanov_table =
\ r
  \  
j \
 -7-6-5-4-3-2-10χ
-1      110
-3       11
-5    12  1
-7   1    1
-9   11   0
-11 11     0
-13        0
-151       -1
| coloured_jones_2 = -q+1+2 q^{-1} -3 q^{-2} + q^{-3} +3 q^{-4} -4 q^{-5} +2 q^{-6} +2 q^{-7} -3 q^{-8} +2 q^{-9} + q^{-10} -3 q^{-11} +2 q^{-12} -2 q^{-14} +2 q^{-15} - q^{-16} - q^{-17} +2 q^{-18} - q^{-19} - q^{-20} + q^{-21} | coloured_jones_3 = - q^{-1} +2 q^{-3} + q^{-4} -2 q^{-5} - q^{-6} +2 q^{-7} +3 q^{-8} -2 q^{-9} -2 q^{-10} + q^{-11} +3 q^{-12} -2 q^{-13} -3 q^{-14} + q^{-15} +4 q^{-16} - q^{-17} -4 q^{-18} +5 q^{-20} -5 q^{-22} - q^{-23} +5 q^{-24} + q^{-25} -5 q^{-26} - q^{-27} +4 q^{-28} + q^{-29} -3 q^{-30} - q^{-31} +3 q^{-32} -2 q^{-34} +2 q^{-36} -2 q^{-38} + q^{-40} + q^{-41} - q^{-42} | coloured_jones_4 = q^5-q^4-q^3-q^2+5- q^{-2} -6 q^{-3} -2 q^{-4} +9 q^{-5} +2 q^{-6} -9 q^{-8} -3 q^{-9} +10 q^{-10} +3 q^{-11} + q^{-12} -10 q^{-13} -3 q^{-14} +11 q^{-15} +3 q^{-16} - q^{-17} -10 q^{-18} -3 q^{-19} +11 q^{-20} +2 q^{-21} -2 q^{-22} -9 q^{-23} -2 q^{-24} +10 q^{-25} +2 q^{-26} -2 q^{-27} -7 q^{-28} -2 q^{-29} +8 q^{-30} +2 q^{-31} -2 q^{-32} -5 q^{-33} - q^{-34} +6 q^{-35} + q^{-36} -3 q^{-37} -3 q^{-38} + q^{-39} +5 q^{-40} -5 q^{-42} -2 q^{-43} +2 q^{-44} +6 q^{-45} -6 q^{-47} -2 q^{-48} + q^{-49} +6 q^{-50} + q^{-51} -4 q^{-52} -2 q^{-53} - q^{-54} +5 q^{-55} -2 q^{-57} - q^{-58} - q^{-59} +4 q^{-60} - q^{-61} - q^{-62} - q^{-63} - q^{-64} +3 q^{-65} - q^{-68} - q^{-69} + q^{-70} | coloured_jones_5 = | coloured_jones_6 = | coloured_jones_7 = | computer_talk = 
In[1]:=    
 
<< KnotTheory`
Loading KnotTheory` (version of August 29, 2005, 15:33:11)...
In[2]:= PD[Knot[10, 132]]
Out[2]:= PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 12, 6, 13], X[15, 18, 16, 19], X[9, 16, 10, 17], X[17, 10, 18, 11], X[13, 20, 14, 1], X[19, 14, 20, 15], X[11, 6, 12, 7], X[2, 8, 3, 7]]
In[3]:= GaussCode[Knot[10, 132]]
Out[3]:= GaussCode[1, -10, 2, -1, -3, 9, 10, -2, -5, 6, -9, 3, -7, 8, -4, 5, -6, 4, -8, 7]
In[4]:= DTCode[Knot[10, 132]]
Out[4]:= DTCode[4, 8, -12, 2, -16, -6, -20, -18, -10, -14]
In[5]:= br = BR[Knot[10, 132]]
Out[5]:= BR[4, {1, 1, 1, -2, -1, -1, -2, -3, 2, -3, -3}]
In[6]:= {First[br], Crossings[br]}
Out[6]:= {4, 11}
In[7]:= BraidIndex[Knot[10, 132]]
Out[7]:= 4
In[8]:= Show[DrawMorseLink[Knot[10, 132]]]
[[Image:10_132_ML.gif]]
Out[8]:= -Graphics-
In[9]:= (#[Knot[10, 132]]&) /@ { SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex }
Out[9]:= {Reversible, 1, 2, 3, NotAvailable, 1}
In[10]:= alex = Alexander[Knot[10, 132]][t]
Out[10]:= -2 1 2 1 + t - - - t + t t
In[11]:= Conway[Knot[10, 132]][z]
Out[11]:= 2 4 1 + 3 z + z
In[12]:= Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]:= {Knot[5, 1], Knot[10, 132]}
In[13]:= {KnotDet[Knot[10, 132]], KnotSignature[Knot[10, 132]]}
Out[13]:= {5, 0}
In[14]:= Jones[Knot[10, 132]][q]
Out[14]:= -7 -6 -5 -4 -2 -q + q - q + q + q
In[15]:= Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]
Out[15]:= {Knot[5, 1], Knot[10, 132]}
In[16]:= A2Invariant[Knot[10, 132]][q]
Out[16]:= -22 -20 -18 -14 -12 2 -8 -6 -q - q - q + q + q + --- + q + q 10 q
In[17]:= HOMFLYPT[Knot[10, 132]][a, z]
Out[17]:= 4 6 4 2 6 2 4 4 3 a - 2 a + 4 a z - a z + a z
In[18]:= Kauffman[Knot[10, 132]][a, z]
Out[18]:= 4 6 3 5 7 2 2 4 2 3 a + 2 a - a z - 4 a z - 8 a z - 5 a z - a z - 7 a z - 6 2 3 3 5 3 7 3 4 4 6 4 6 a z + 9 a z + 19 a z + 10 a z + 10 a z + 10 a z - 3 5 5 5 7 5 4 6 6 6 3 7 5 7 6 a z - 12 a z - 6 a z - 6 a z - 6 a z + a z + 2 a z + 7 7 4 8 6 8 a z + a z + a z
In[19]:= {Vassiliev[2][Knot[10, 132]], Vassiliev[3][Knot[10, 132]]}
Out[19]:= {3, -5}
In[20]:= Kh[Knot[10, 132]][q, t]
Out[20]:= -3 1 1 1 1 1 1 1 1 q + - + ------ + ------ + ------ + ----- + ----- + ----- + ----- + q 15 7 11 6 11 5 9 4 7 4 9 3 5 3 q t q t q t q t q t q t q t 2 1 ----- + --- 5 2 q t q t
In[21]:= ColouredJones[Knot[10, 132], 2][q]
Out[21]:= -21 -20 -19 2 -17 -16 2 2 2 3 1 + q - q - q + --- - q - q + --- - --- + --- - --- + 18 15 14 12 11 q q q q q -10 2 3 2 2 4 3 -3 3 2 q + -- - -- + -- + -- - -- + -- + q - -- + - - q 9 8 7 6 5 4 2 q q q q q q q q
}}