%0 Generic %1 Carter2009a %A Carter, J. Scott %A Oshiro, Kanako %A Saito, Masahico %D 2009 %K algebra homology knot-theory quandles topology %T Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces %U http://arxiv.org/abs/0905.3374 %X 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.

@misc{Carter2009a, 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.}, added-at = {2009-05-22T12:47:57.000+0200}, author = {Carter, J. Scott and Oshiro, Kanako and Saito, Masahico}, biburl = {https://www.bibsonomy.org/bibtex/28996b2bbbe5c3696410b489210f8b281/njj}, description = {Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces}, interhash = {75498c9e2d46794349ba2cb1f0317db0}, intrahash = {8996b2bbbe5c3696410b489210f8b281}, keywords = {algebra homology knot-theory quandles topology}, note = {cite arxiv:0905.3374 }, timestamp = {2009-05-22T12:47:57.000+0200}, title = {Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces}, url = {http://arxiv.org/abs/0905.3374}, year = 2009 }