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The ability to incrementally learn new classes is crucial to the development of real-world artificial intelligence systems. In this paper, we focus on a challenging but practical few-shot class-incremental learning (FSCIL) problem. FSCIL requires CNN models to incrementally learn new classes from very few labelled samples, without forgetting the previously learned ones. To address this problem, we represent the knowledge using a neural gas (NG) network, which can learn and preserve the topology of the feature manifold formed by different classes. On this basis, we propose the TOpology-Preserving knowledge InCrementer (TOPIC) framework. TOPIC mitigates the forgetting of the old classes by stabilizing NG's topology and improves the representation learning for few-shot new classes by growing and adapting NG to new training samples. Comprehensive experimental results demonstrate that our proposed method significantly outperforms other state-of-the-art class-incremental learning methods on CIFAR100, miniImageNet, and CUB200 datasets.