Betti numbers of a class of barely G2 manifolds

TL;DR

This paper explicitly computes the Betti numbers for a specific class of barely G2 manifolds constructed from Calabi-Yau complete intersections and free involutions, advancing understanding of their topological properties.

Contribution

It provides explicit calculations of Betti numbers for barely G2 manifolds formed from Calabi-Yau complete intersections with free involutions, a novel class of examples.

Findings

Betti numbers are explicitly calculated for the class of barely G2 manifolds.

The manifolds are constructed from Calabi-Yau complete intersections in product spaces.

The involutions considered are free and act on the Calabi-Yau manifolds.

Abstract

We calculate explicitly the Betti numbers of a class of barely G2 manifolds - that is, G2 manifolds that are realised as a product of a Calabi-Yau manifold and a circle, modulo an involution. The particular class which we consider are those spaces where the Calabi-Yau manifolds are complete intersections of hypersurfaces in products of complex projective spaces and the involutions are free acting.