Q-fundamental surfaces in lens spaces

We determine all the Q-fundamental surfaces in $(p,1)$-lens spaces and $(p,2)$-lens spaces with respect to natural triangulations with $p$ tetrahedra. For general $(p,q)$-lens spaces, we give an upper bound for elements of vectors which represent Q-fundamental surfaces with no quadrilateral normal disks disjoint from the core circles of lens spaces. We also give some examples of non-orientable closed surfaces which are Q-fundamental surfaces with such quadrilateral normal disks.