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

2009/05/20 by Carter, J. Scott, Oshiro, Kanako, Saito, Masahico · 1 citation
#57M27 #57Q45 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0905.3374

Abstract

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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• Good involutions of twisted conjugation subquandles and Alexander quandles

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