Reconstructing the intricate local morphology of neurons and their long-range projecting axons can address many connectivity related questions in neuroscience. The main bottleneck in connectomics pipelines is correcting topological errors, as multiple entangled neuronal arbors is a challenging instance segmentation problem. More broadly, segmentation of curvilinear, filamentous structures continues to pose significant challenges. To address this problem, we extend the notion of simple points from digital topology to connected sets of voxels (i.e. supervoxels) and propose a topology-aware neural network segmentation method with minimal computational overhead. We demonstrate its effectiveness on a new public dataset of 3-d light microscopy images of mouse brains, along with the benchmark datasets DRIVE, ISBI12, and CrackTree.