The Betti numbers of real toric varieties associated to Weyl chambers of types E7 and E8

TL;DR

This paper calculates the rational Betti numbers of real toric varieties linked to Weyl chambers of types E7 and E8, completing the classification for all root system types.

Contribution

It provides the first complete computation of Betti numbers for these complex real toric varieties associated with E7 and E8 root systems.

Findings

Betti numbers for E7 and E8 real toric varieties computed

Completes the classification for all root system types

Advances understanding of topological invariants in algebraic geometry

Abstract

We compute the rational Betti numbers of the real toric varieties associated to Weyl chambers of types $E_7$ and $E_8$, completing the computations for all types of root systems.