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Topological strategies for navigation meaningfully reduce the space of possible actions available to a robot, allowing use of heuristic priors or learning to enable computationally efficient, intelligent planning. The challenges in estimating structure with monocular SLAM in low texture or highly cluttered environments have precluded its use for topological planning in the past. We propose a robust sparse map representation that can be built with monocular vision and overcomes these shortcomings. Using a learned sensor, we estimate high-level structure of an environment from streaming images by detecting sparse vertices (e.g., boundaries of walls) and reasoning about the structure between them. We also estimate the known free space in our map, a necessary feature for planning through previously unknown environments. We show that our mapping technique can be used on real data and is sufficient for planning and exploration in simulated multi-agent search and learned subgoal planning applications.