Minimal Balanced Triangulations of Sphere Bundles over the Circle

Abstract

We determine the minimum number of vertices needed to provide balanced triangulations of ${\mathbb{S}}^{d-2}$-bundles over ${\mathbb{S}}^1$. If $d$ is odd and the bundle is orientable, or $d$ is even and the bundle is non-orientable, the minimum number of vertices is $3d$; otherwise, it is $3d+2$. Similar results apply to all balanced simplicial complexes that triangulate homology manifolds with ${\beta }_1\ne 0$ and ${\beta }_2=0$, where ${\beta }_i$'s are the Betti numbers, computed with coefficients in $\mathbb{Q}$.

10 pages

References in corpus (1)

• Lower Bound Theorems and a Generalized Lower Bound Conjecture for balanced simplicial complexes

Cited by in corpus (1)

• Lower Bound Theorems and a Generalized Lower Bound Conjecture for balanced simplicial complexes