Let $\omega$ be a connection form on $F(M)$ and let $\theta$ be the solder form, where a frame is written as an isomorphism $u:\mathbb R^n \to T_xM$ and the right action is $u\cdot g=u\circ g$. The torsion form $T=d\theta+\omega\wedge\theta$ is horizontal and satisfies $(R_g)^*T=g^{-1}T$ for $g \in GL(n,\mathbb R)$, with $g^{-1}$ acting by the standard representation on $\mathbb R^n$. Hence $T$ corresponds, under the associated-bundle convention $F(M)\times_{GL(n,\mathbb R)}\mathbb R^n \cong TM$, to a section of $\Lambda^2T^*M \otimes TM$. If $\nabla$ is the induced connection on $TM$, then the corresponding tensor is $\operatorname{Tor}_{\nabla}(X,Y)=\nabla_XY-\nabla_YX-[X,Y]$ for vector fields $X,Y \in \mathfrak X(M)$.