In digital pathology, segmenting densely distributed objects like glands and nuclei is crucial for downstream analysis. Since detailed pixel-wise annotations are very time-consuming, we need semi-supervised segmentation methods that can learn from unlabeled images. Existing semi-supervised methods are often prone to topological errors, e.g., missing or incorrectly merged/separated glands or nuclei. To address this issue, we propose TopoSemiSeg, the first semi-supervised method that learns the topological representation from unlabeled histopathology images. The major challenge is for unlabeled images; we only have predictions carrying noisy topology. To this end, we introduce a noise-aware topological consistency loss to align the representations of a teacher and a student model. By decomposing the topology of the prediction into signal topology and noisy topology, we ensure that the models learn the true topological signals and become robust to noise. Extensive experiments on public histopathology image datasets show the superiority of our method, especially on topology-aware evaluation metrics.