Understanding the Chow-Rashevsky Theorem

Question

I'm trying to understand the Chow-Rashevsky Theorem. I unfortunately do not have a formal knowledge of what's going on but have figured out most of the terms.

Basically a system $\Sigma$ must satisfy the Chow condition:

$$\mathtt{Lie}(X_1, \ldots, X_m)(q) = T_qM, \hspace{1em} \forall q\in M. $$

where $M$ is a manifold. But I cannot find a definition for $T_q$.

I think it is a linear transformation. Am I correct?

Answer 1

Googling extensively led me to this - apparently $T_q$ is the tangent space of the manifold.

More details here.