Geometric group theory

Geometric group theory studies mathematical groups by examining how they can be represented as shapes and spaces, revealing their structure through geometry. It analyzes how groups act on geometric objects, like graphs or spaces, to understand their properties, such as symmetry and complexity. This approach allows mathematicians to visualize abstract algebraic concepts spatially, making it easier to see relationships and classify groups based on their geometric behavior. Essentially, it connects algebra and geometry to provide deeper insights into the nature of mathematical groups.