Title: Active Topological Mapping by Metric-Free Exploration via Task and Motion Imitation. Abstract: Topological map is an effective environment representation for visual navigation. It is a graph of image nodes and spatial neighborhood edges without metric information such as global or relative agent poses. However, currently such a map construction relies on either less-efficient random exploration or more demanding training involving metric information. To overcome these issues, we propose active topological mapping (ATM), consisting of an active visual exploration and a topological mapping by visual place recognition. Our main novelty is the simple and lightweight active exploration policy that works entirely in the image feature space involving no metric information. More specifically, ATM's metric-free exploration is based on task and motion planning (TAMP). The task planner is a recurrent neural network using the latest local image observation sequence to hallucinate a feature as the next-step best exploration goal. The motion planner then fuses the current and the hallucinated feature to generate an action taking the agent towards the hallucinated feature goal. The two planners are jointly trained via deeply-supervised imitation learning from expert exploration demonstrations. Extensive experiments in both exploration and navigation tasks on the photo-realistic Gibson and MP3D datasets validate ATM's effectiveness and generalizability.