Plumbing

The plumbing of a $p$-sphere and a $q$-sphere is defined as the disjoint union of $\Bbb{S}^p\times\Bbb{S}^q$ and $\Bbb{D}^p\times\Bbb{S}^q$ with their common $\Bbb{D}^p\times\Bbb{D}^q$, identified via the identity homeomorphism.

See also Hypersphere

References

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 180, 1976.