Abstract
This project aims to study the construction of the homotopic invariant \nu(\varphi) of a G_2-structure \varphi acting on the tangent bundle of a closed 7-manifold, as well as the demonstration that, for manifolds with G_2 holonomy obtained through a twisted connected sum, the associated torsion-free G_2-structure always has \nu(\varphi) = 24. We will also see the construction of the homot…