Prime decomposition of 3-manifolds

The prime decomposition of 3-manifolds is a fundamental concept in the field of 3-manifold topology. It states that any compact connected 3-manifold can be uniquely decomposed into a connected sum of prime 3-manifolds, with the understanding that the connected summands are considered up to homeomorphism. ### Key Concepts: 1. **3-Manifold**: A 3-manifold is a space that locally looks like Euclidean 3-dimensional space.