# cap off

## English

### Verb

cap off (third-person singular simple present caps off, present participle capping off, simple past and past participle capped off)

1. (transitive) To finish by making one last addition.
2. () To glue a relatively uncomplicated compact manifold to a manifold of the same dimension along (a component of the latter's boundary).
• a. 1997, Rob[ion] Kirby, "Problems in Low-Dimensional Topology", problem 3.21, in, 1997, William H[ilal] Kazez, editor, Geometric Topology, proceedings of the 1993 Georgia International Topology Conference, AMS/IP Studies in Advanced Mathematics 2, American Mathematical Society, →ISBN, part 2, page 163,
Let ${\displaystyle X}$ be an acyclic 2-complex and ${\displaystyle M_{0}^{3}}$ an abstract regular neighborhood of ${\displaystyle X}$; ${\displaystyle \partial M_{0}=S^{2}}$, so cap off to get a homology ${\displaystyle 3}$-sphere ${\displaystyle M^{3}}$.
• a. 1997, Michael T. Anderson, "Scalar Curvature and Geometrization Conjectures for 3-Manifolds", in, 1997, Karsten Grove and Peter Petersen, editors, Comparison Geometry, Mathematical Sciences Research Institute Publications 30, →ISBN, page 53,
Note, however, that when one cuts a 3-manifold along an incompressible torus, there is no canonical way to cap off the boundary components thus created, as is the case for spheres. For any toral boundary component, there are many ways to glue in a solid torus... .
• 1997, W[illiam] B[ernard] Raymond Lickorish, An Introduction to Knot Theory, Graduate Texts in Mathematics 175, Springer, →ISBN, page 61,
Cap off, with discs just above the annulus, any circuits that bound in the annulus; then use annuli to cap off adjacent pairs of curves that encircle the annulus in opposite directions.