Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces

Details Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces

2009-05-20

arxiv.org/abs/0905.3374v3

Mathematics

Geometric Topology

Error in quandle table repaired, and spurious figures removed

Scientific paper

Quandles with involutions that satisfy certain conditions, called good involutions, can be used to color non-orientable surface-knots. We use subgroups of signed permutation matrices to construct non-trivial good involutions on extensions of odd order dihedral quandles. For the smallest example of order 6 that is an extension of the three-element dihedral quandle, various symmetric quandle homology groups are computed, and applications to the minimal triple point number of surface-knots are given.

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