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Henry Bushby Transcription Pages

VM533B94v6_233.jpg

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233
(iv) N = X.
n = 1 + 1 x X = 11.
Ans =I2 10B/10C (z = 2) torsion & plait
I3 5B/10C (z = 1) plait
I6 2B/10C (z = 2) plait
I11 1B/10C (z = 1) plait (twist)
II3 5B/10C (z = 1) torsion
II11 1B/10C (z = 1) twist
V6 2B/10C (reduces) (z = 2) torsion
V11 1B/10C (z = 1) twist
X11 1B/10C (z = 1) (torsion),(twist)
[Therefore symbol] 4 5 genuine knots result = f/2 - 1.
= (no. of factors of^twists reduce y + 1) subtracted from the total no. of^nominal knots.
 ? is there always a reducible knot?
Again y = 6, find Nn
Values of N = 1, 2, 3, 6 = N
Augmented 2, 3, 4, 7 =n
(1) N = I.
n = 1 + 1 x I = 2
n = 1 + 2 x I = 3
n = 1 + 3 x I = 4
n = 1 + 6 x I = 7
[to right of previous 4 lines]
4 genuine knots are
I2 6B/6C z = 2
I3 3B/6C z = 3
I4 2B/6C z = 2
I2 3B/6C z = 3
Ans I2 6B/6C, I3 3B/6C, I4 2B/6C, I7 1B/6C, II3 3B/6C, II7 1B/6C, III4 2B/6C, VI7 1B/6c

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