We present a hybrid visualization technique that integrates maps into network visualizations to reveal and analyze diverse topologies in geospatial movement data. With the rise of GPS tracking in various contexts such as smartphones and vehicles there has been a drastic increase in geospatial data being collect for personal reflection and organizational optimization. The generated movement datasets contain both geographical and temporal information, from which rich relational information can be derived. Common map visualizations perform especially well in revealing basic spatial patterns, but pay less attention to more nuanced relational properties. In contrast, network visualizations represent the specific topological structure of a dataset through the visual connections of nodes and their positioning. So far there has been relatively little research on combining these two approaches. Shifted Maps aims to bring maps and network visualizations together as equals. The visualization of places shown as circular map extracts and movements between places shown as edges, can be analyzed in different network arrangements, which reveal spatial and temporal topologies of movement data. We implemented a web-based prototype and report on challenges and opportunities about a novel network layout of places gathered during a qualitative evaluation.