This work presents a non-geometrical navigation approach based on a purely topological understanding of underground environments. By conceptualizing subterranean scenarios as a set of tunnels that intersect with each other, and taking a navigation approach based on topological instructions, we simplify the navigation problem to the sequential execution of human-understandable instructions. This approach is built on top of a lightweight Convolutional Neural Network (CNN) that processes the readings of a 3D LiDAR sensor and produces an estimation of the angular positions of the surrounding tunnels with respect to the robot. As a result of this approach, our method can navigate these underground environments by only being provided with the necessary topological instructions, without the need for a map, or for building one during navigation. Additionally, it can also rely on a lightweight graph representation of the environment. This graph can be either defined by the user, generated during navigation or explicitly built in an exploration task. To showcase these capabilities, this article provides an experimental evaluation of the method both in simulation and in a real environment.