Equilibrium and equivariant triangulations of some small covers with minimum number of vertices

Abstract

Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal ${\mathbb{Z}}_2^2$-equivariant triangulations of $2$-dimensional small covers. We discuss vertex minimal equilibrium triangulations of ${\mathbb{RP}}^3\#{\mathbb{RP}}^3$, $S^1\times {\mathbb{RP}}^2$ and a nontrivial $S^1$ bundle over ${\mathbb{RP}}^2$. We construct some nice equilibrium triangulations of the real projective space ${\mathbb{RP}}^n$ with $2^n+n+1$ vertices. The main tool is the theory of small covers.

15 pages, 10 figures, minor changes, accepted for publication in Journal of the Ramanujan Mathematical Society

References in corpus (1)

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

Cited by in corpus (2)

• A subexponential size triangulation of $\mathbb{R}{P}^n$
• On $\ZZ_2^n$-equivariant triangulation of $\RR P^n$