Cobordism

Cobordism is a concept in mathematics that studies how different shapes or spaces can be connected through a higher-dimensional "bridge." Imagine two surfaces sitting in space; they are cobordant if there's a smooth, continuous shape that connects them in one higher dimension, like a tunnel linking the two. This idea helps mathematicians understand relationships between shapes and classify them based on how they can be smoothly transformed into each other through these higher-dimensional connections. Essentially, cobordism provides a way to analyze the properties of shapes by examining how they can be related through these bridging structures.