On $\ZZ_2^n$-equivariant triangulation of $\RR P^n$

TL;DR

This paper investigates $bZ_2^n$-equivariant triangulations of real projective spaces, revealing how they induce subdivisions of the orbit space and establishing minimal vertex counts for specific cases.

Contribution

It demonstrates the relationship between equivariant triangulations and orbit space subdivisions, and determines the minimal vertices for a $bZ_2^3$-equivariant triangulation of $bRP^3$.

Findings

Equivariant triangulations induce subdivisions of the orbit space.

Minimal vertex count for $bZ_2^3$-equivariant triangulation of $bRP^3$ is 11.

Triangulation properties depend on the group action and space structure.

Abstract

We study several properties of $\ZZ_2^n$-equivariant triangulations of $\RR P^n$. We show that a $\ZZ_2^n$-equivariant triangulation of $\RR P^n$ induces a triangulated subdivision of the orbit space $\bigtriangleup^n$. We show that any vertex minimum $\ZZ_2^3$-equivariant triangulation of $\RR P^3$ contains $11$ vertices.