Minimal triangulations of (S^3\times S^1)^{#3} and (S^3 \(twisted product) S^1)^{#3}

Abstract

A triangulated $d$-manifold $K$, satisfies the inequality $\left(\genfrac{}{}{0ex}{}{f_0(K)-d-1}{2}\right)\ge \left(\genfrac{}{}{0ex}{}{d+2}{2}\right){\beta }_1(K;{\mathbb{Z}}_2)$ for $d\ge 3$. The triangulated $d$-manifolds that meet the bound with equality are called {\em tight neighborly}. In this paper, we present tight neighborly triangulations of 4-manifolds on 15 vertices with ${\mathbb{Z}}_3$ as automorphism group. One such example wasconstructed by Bagchi and Datta in 2011. We show that there are exactly 12 such triangulations up to isomorphism, 10 of which are orientable.

20 pages

References in corpus (1)

• An infinite family of tight triangulations of manifolds