Non-orientable 3-manifolds of small complexity (Q1408722)

If \(M\) is a \(\mathbb{P}^2\)-irreducible compact 3-manifold and not \(S^3\), \(\mathbb{RP}^3\), or \(L_{3,1}\), the complexity of \(M\), \(c(M)\), is the smallest number of tetrahedra possible in a triangulation of \(M\). The authors examine such 3-manifolds \(M\) with \(c(M)\leqslant 7\). They show there are none with \(c(M)\leqslant 5\), 4 with \(c(M)=6\), and when \(c(M)=7, M\) can be \(\mathbb{H}^2\times S^1\) or of type \textbf{Sol} or have a non-trivial \textbf{JSJ} decomposition.