Criminal activities cause considerable harm to victims and their communities. The insights gained from police department records can be used to understand criminal behavior, predict crime hotspots, forecast criminal events, prevent crime activity, and ultimately foster safer communities. Recently, there has been a growing interest in developing and applying deep learning (DL) models for crime forecasting by leveraging neural network architectures to identify key spatiotemporal dependencies and patterns shared across different crime series. However, these models often struggle to capture local topological information and higher-order interactions within both spatial and temporal domains. Additionally, they fail to fully leverage multi-modal data, limiting their ability to uncover hidden relationships among different crime incidents. To address these challenges, this paper introduces the Large Language Model-Based Zigzag Graph Neural Networks (LLM-ZGNNs) for highly efficient and effective spatiotemporal crime forecasting. More specifically, to integrate time-aware topological information into the DL architecture, we introduce the multi-zigzag topological tensor using zigzag persistent homology. We also utilize the LLM with a carefully designed prompt to enhance the visual knowledge extraction from satellite images to improve performance in predicting crime event frequency. Experiments on real-world crime data show LLM-ZGNNs outperforms state-of-the-art models by a significant margin. Additionally, we explore the relationship between homelessness and the criminal justice system by establishing an open knowledge network, addressing the knowledge gap and examining strategies to protect individuals experiencing homelessness from crime.