Knot Complements

Twister was used to produce a census of hyperbolic surface bundles over the circle for the surfaces S_{g,1} with 1 ≤ g ≤ 5. Bundles that are knot complements were then identified by performing a Dehn filling and checking the fundamental group. The depth to which each census was calculated is shown in the table below.

Genus	Census depth
1	2
2	10
3	14
4	14
5	14

Each hyperbolic, fibred knot complement listed on knotinfo was then checked against the manifolds on the census and a monodromy found where possible. Monodromies were found for approximately 63% of the knots listed and a complete summary of the results obtained is available here. (Last updated: 18/03/2013)

Note that, as the list of fibred knot complements built was a complete census, if a monodromy was not found for a particular knot then it cannot have a monodromy consisting of  2 / 10 / 14 / 14 /14 or fewer characters (depending on its three genus).

The generating sets that were used are shown below and in each case the generators are ordered: a < A < b < B < … < l < L for computational reasons.

Generators of S_{1,1}

Generators of S_{2,1}

Generators of S_{3,1}

Generators of S_{4,1}

Generators of S_{5,1}

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