Q-fundamental surfaces in lens spaces

TL;DR

This paper classifies all Q-fundamental surfaces in certain lens spaces and provides bounds and examples for more general cases, advancing understanding of normal surface theory in 3-manifolds.

Contribution

It explicitly determines Q-fundamental surfaces in (p,1) and (p,2) lens spaces and offers bounds and examples for general (p,q)-lens spaces.

Findings

Complete classification of Q-fundamental surfaces in (p,1) and (p,2) lens spaces.

Upper bounds for vectors representing Q-fundamental surfaces in general lens spaces.

Examples of non-orientable Q-fundamental surfaces with specific quadrilateral disks.

Abstract

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.