Equilibrium triangulations of some quasitoric 4-manifolds

TL;DR

This paper extends the construction of equilibrium triangulations from complex projective spaces to a broader class of 4-dimensional quasitoric manifolds, achieving vertex minimal triangulations in some cases.

Contribution

It generalizes the known equilibrium triangulation of  to a wider class of quasitoric manifolds, providing new minimal triangulations.

Findings

Constructed equilibrium triangulations for several 4-dimensional quasitoric manifolds.

Achieved vertex minimal equilibrium triangulations in some cases.

Extended the 10-vertex triangulation of  to more complex manifolds.

Abstract

Quasitoric manifolds, introduced by M. Davis and T. Januskiewicz in 1991, are topological generalizations of smooth complex projective spaces. In 1992, Banchoff and K\"uhnel constructed a 10-vertex equilibrium triangulations of $\CP^2$. We generalize this construction for quasitoric manifolds and construct some equilibrium triangulations of $4$-dimensional quasitoric manifolds. In some cases, our constructions give vertex minimal equilibrium triangulations.