Geometric topology is a branch of mathematics that studies the properties of spaces that are preserved under continuous transformations, such as stretching or bending, but not tearing or gluing. It focuses on the shapes and structures of objects, often using concepts from geometry and algebra to understand their properties. One of the key areas in geometric topology is the study of manifolds, which are spaces that locally resemble Euclidean space. Researchers also explore knot theory, which examines the properties of knots and links in three-dimensional space, revealing insights into both mathematics and applications in fields like biology and physics.