A lens space is a specific type of three-dimensional manifold that can be thought of as a generalization of the notion of a solid torus. More formally, lens spaces are a class of manifolds that can be defined using the quotient of the 3-sphere \( S^3 \) by a specific action of the group \( \mathbb{Z}/p\mathbb{Z} \), where \( p \) is a positive integer.
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For coprime integers and , the lens space is the quotient of by . Equivalently, it is obtained by an appropriate rational surgery on the unknot.