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We use classical obstruction theory \`{a} la Eilenberg-Steenrod to obtain ahomotopy classification of $\mathrm{Spin}(7)$-structures on compact$8$-manifolds with abelian fundamental group. As an application, we show that acompact, connected Riemannian $8$-manifold with holonomy contained inside thegroup $\mathrm{Spin}(7)$ has exactly two $\mathrm{Spin}(7)$-structuresextending the induced $G_{2}$-structure on the boundary.

A homotopy classification of $\mathrm{Spin}(7)$-structures with applications to exceptional Riemannian holonomy