The Betti numbers of real toric varieties associated to Weyl chambers of type $B$

TL;DR

This paper calculates the rational Betti numbers of real toric varieties linked to Weyl chambers of type B and proves their integral cohomology lacks p-torsion for all odd primes.

Contribution

It provides explicit Betti number computations and establishes torsion-freeness of integral cohomology for these specific toric varieties.

Findings

Rational Betti numbers are explicitly computed.

Integral cohomology is p-torsion free for all odd primes p.

Enhances understanding of topological properties of type B Weyl chamber associated toric varieties.

Abstract

We compute the (rational) Betti number of real toric varieties associated to Weyl chambers of type $B$. Furthermore, we show that their integral cohomology is $p$-torsion free for all odd primes $p$.